Never before during his ghastly existence had Peeves seen Dumbledore angry. Coincidentally, Peeves had also never encountered a headmaster who could stand up to him. Now that he was floating face-to-wand with the old wizard and confronted with the prospect of imminent erasure, he was quite wishing that he hadn't set him off.
"Try as you may, try as you might, your moaning can't fix what just isn't right," he chuckled, bowing with a flourish.
If he was going to cease existing, Peeves supposed that he should at least go out with a lark. To his moderate surprise, Dumbledore lowered his wand. His rage-hardened face slowly softened into something unreadable, and he redirected his focus to the floor. At his feet there was a shattered amalgamation of glass, water solution, and fake snow. With a breath, the greying wizard raised his eyes to meet Peeves's gaze once again, any signs of his former outburst completely void from his face.
"My apologies for the outburst, Peeves," he stated cordially, turning his back on the poltergeist and beginning to walk towards the opposite end of his office, "surely, that will not have left you with the best impression of me."
Peeves guffawed, falling backwards only to catch himself mid-air.
"You really gave ol' Peeves a scare!" Peeves screeched, "perhaps our great headmaster is more of a mischief maker than the old bat lets on!"
He gleefully shot backwards in the air, spiraling around the book-lined walls of the study and sending a few leathery tomes tumbling to the floor in his wake. With each loud and satisfying thud he looked to Dumbledore, trying to gauge his reaction. There was none. The elderly wizard had picked up a dust pan and its accompanying hand broom and was beginning to make his way back towards the pile of glass.
"I think you'll find that there is more to this world than laws and lawbreakers, mister Peeves," offered Dumbledore.
The old wizard had begun deftly sweeping the shattered glass and fake snow into his dust pan, ignoring the water solution for the time being. Dumbledore's wand sat in its holster as he worked and he made no move to use it. Meanwhile, Peeves had been occupying himself by floating above the headmaster and scrutinizing his snowglobe collection. It was strange that in a room whose walls were book shelves, one singular space had been dedicated to housing snowglobes. While his original intent had been to throw another of the precious items onto Dumbledore's head as he worked, Peeves found himself distracted by the intricacies of each globe.
There were seven of them in total, and they were all seemingly handmade. Each one had an ornate wooden base that was carved and treated differently from the last, and there was a visible increase in craftmanship between the first and last globe. Each of the items contained a tiny scene. The first snow globe only showed a simple house that looked like it had been made from clay, but the final one contained a small town. Tiny things like asymmetry between buildings showed the poltergeist that these were all also handmade. Now that he was looking, Peeves had noticed another oddity. The glass on each of the treasures had been polished. While this in and of itself shouldn't seem unusual, the slight smudging on the glass told Peeves that it had been polished by hand. Each of these things led Peeves to one distinct conclusion. He laughed and slapped a book off of the shelf below him, sending it tumbling towards the headmaster.
"Dumbly's scared of ma-gic, Dumbly's scared of ma-gic!" he sing-songed in his shrill, ear-piercing voice.
Just as he finished his last taunt, Dumbledore raised his wand and with a noncommittal motion and a mumbled "flipendo" sent the book skittering to the floor behind him.
"Hey!" demanded Peeves, "what's all this, then?"
Just as he was about to knock a snow globe to the floor Dumbledore stood back up, dustpan in hand.
"Those globes belonged to someone who was quite dear to me," he explained, "she was not terribly fond of magic."
Peeves, hand still raised to smite a second globe from its perch, watched the elderly wizard as he emptied his dustpan into a wastebin near his desk. From there, Dumbledore went and retrieved a mop and bucket. A wizard using a mop with his hands? What kind of a world did Peeves suddenly find himself in? Surely the man could have at least summoned a house elf.
"That's bologna," decided Peeves, swatting another globe from the shelf, "and I'm bored."
Dumbledore caught the globe this time, dropping the mop in the process. Seeing this, Peeves cackled and shook the entire shelf before speeding off. Dumbledore stood there in a mess of shattered globes, holding the only survivor in his spare hand.
He should have banished Peeves then and there. The poltergeist wasn't even a real ghost; he was an effigy of mischief that had been crafted from years of misbehaving students. Dispelling him and freeing the castle of his curse would be an act that almost universally bettered the people whom he was now meant to care for, but he was not willing to do it. This effigy had a human face. It had a face, a name, and even displayed some range of human emotion. Death was no stranger to Albus Dumbledore, but he wished that it had been. Furthermore, exploding at someone and hurting them was most certainly the last thing that should be done in honor of the snow globes. Ariana would not have wanted it that way.
Still, Dumbledore knew that he had to establish himself as the headmaster. It was as such that when Peeves reappeared, the elderly wizard knew exactly what he needed to do.
"Is Dumbly gonna cry?" cackled Peeves, "I've broken 'is precious treasures that remind him of a la-dy!"
"Ah, yes," stated Dumbledore, "Peeves. I'm glad that I was able to catch you before you left."
Placing the mop bucket onto the floor, Dumbledore withdrew his wand. Peeves watched on, a massive grin practically tearing his face apart.
"A' you gonna test somethin' on me?" he giggled, dancing in place, "go on then, let's see it! The others just gave up but let's see what you've got!"
"Silencio," stated Dumbledore, flicking his wand in a μ motion.
Peeves doubled over in silent laughter, clutching his stomach for support. He mouthed something, but Dumbledore couldn't tell what it was for the life of him. Just as the poltergeist raised his hand to slap some books off of the nearest shelf, Dumbledore muttered another incantation. This particular spell was home brewed.
"Intactillis," he commanded, tracing the outline of an hourglass with his wand but leaving the bottom of the shape unconnected.
Peeves's hand passed directly through the book behind him, and the entity blanched. In that moment, the poltergeist was the literal definition of "turning ghostly pale." He whipped his head around frantically, glaring holes into the book shelf as he tried repeatedly to knock a book from its perch. As this was happening, Dumbledore returned his desk and placed the remaining snowglobe near a stack of personal books to the left. Once he returned, Peeves was about done with his tantrum. At this point, the poltergeist turned his attention to Dumbledore and fell to his knees on the ground -rather, floating about one centimeter above it-, clasping his hands together and raising them to his forehead in an exaggerated begging motion.
"We should plan to meet again in one week's time," said Dumbledore.
He returned to his spot by the shattered snowglobes and began to clean them up as Peeves watched on, utter disbelief painting his face.
A/N: I hope that was alright! I imagine that Ariana found comfort in snowglobes because she had complete control over the tiny, contained settings. They were bottled up and peaceful, not at risk of hurting anybody.