Disclaim: I do not own Harry Potter or any of the characters and I respect JK Rowling.
Experiment no. 1 The settings.
After the war, everyone changes a little bit, not much, but fundamentally, so, yeah, I guess you can say a lot. It's what war did to people.
Hermione Granger had it all, she was no longer a prude nor stubborn (never had been in her own words), she was happy. Not that any loss in the war didn't mean anything to her, it meant a lot to her, she even hated herself for having such a wonderfully good memory, she could count alphabetically, geographically (of birth place), from young to old of the people she knew was dead, she was presented for some of the deaths. Her parents spells were now irreversible, and now she was only a niece to them that they treated as daughter (she couldn't reverse the spells didn't mean she couldn't give them new ones). Everything was so heavy, so sad, so miserable, and she had it all, her brain had to stop from being overload. She even had to pick up little pieces of her friends, apparently, being alive wasn't good enough for them. She tried to be happy, be the 18-year-old she was supposed to be.
Ronald Weasley wasn't happy, after the second wizarding war, he dated Hermione for 2 months, but not actually dating, Ronald was helping his family to come back to life, literally. Molly was moaning a lot, even Ginny, the bright little sunshine of the family went depressed. All Ron could think of was his family. Weasley's Wizard Wheezes went to George and him, Ronald Weasly, who finally showed what a true Griffindor he is, has taken over the family. He couldn't understand why Hermione would want to go back to Hogwarts, couldn't understand why she could laugh while his whole family wasn't, and in the 2 months that he was dating Hermione, she couldn't fight with him. She understood everyone took things differently, what she did seem phony and insensitive to him, and she understood it, he understood it, for the first time in life, they agreed with peace, that they had to break up.
Harry Potter had a little break, Hermione suggested it. After the war, he didn't want any attention anymore, fighting scared him a little, but he was a Griffindor, he would come around, he just needed a little break. Hermione saw it, she knew what he was thinking even if he wasn't speaking out loud. After destroying the elder wand, Hermione suggested him, if he wanted to go, now will be the best time. So he went, apparently his family had a little property in Greece, in a small village where James wanted to take Lily for their honeymoon, which they never had a chance to. So off he went, Hermione was alone.
Draco Malfoy also had it all. His family wanted to leave the country, to avoid prison time, and he was sick of hiding. He told his parents either leave without him or stayed and face the trials, he prided himself as a Slytherine, he knew everything came with a price, and leaving came with a price of losing everything else, the Malfoy name and fortune, the freedom to be seen and a chance of redemption. Leaving, will cost him living with guilt and shame forever, for his attempt to kill his Headmaster, for how many lives he killed as a death eater, for his cowardliness. He must stayed, he faced the trials, and so have his family. His father got 50 years, his mother got a probation for 5 years, and he got clear of all charges, for being underage, for aiding the escape of the golden trio, for turning his family in, for turning himself in.
As a matter of fact, all underage wizards were clear of all charges, as the loss in numbers in the wizarding world was too high. They needed new blood to rebuild this world, that all who had fought in the final battle could become Aurors without getting their N.E.W.T. s as a reward.
And so, everything was set into motion. A Hermione without Harry and Ron, a Draco without the Malfoy family, in Hogwarts.