DEATH OF A DETECTIVE: SOLUTION
1) Diabetic shock. 2) Her sister, Miara Larte. 3) Miara tampered with Kaeden's diabetes medication and switched the artificial sweetener with real sugar.
The insulin, needles, emergency candies, and low-sugar diet lead to one explanation: Kaeden Larte was a diabetic. Once the fugitives figured this out they knew there was only one person who could have killed her. Who was the only one who could have known about Kaeden's diabetes? And who didn't instantly mention it when she collapsed? Miara Larte, Kaeden's sister and her killer.
Kaeden kept her condition a secret for fear it would affect her ability to work as a police detective, and took the proper precautions to ensure her illness wouldn't rear its head while she was on the clock. She carried her medication and a supply of sugary candy for emergencies, and she was vigilant with her diet to manage blood sugar. As her sister Miara of course knew about the diabetes and happily kept Kaeden's secret. The two of them had only each other since they were children. But when Kaeden passed her inspector's exam and prepared to move away, Miara saw red. How dare her sister abandon her after all these years! Quickly she saw how Kaeden's secret could be turned into the perfect murder weapon.
Miara began by switching Kaeden's insulin with tap water, rendering the injections useless and causing her blood sugar to skyrocket. Kaeden definitely felt the symptoms, but with the Raada police department's physical examination looming a doctor's visit would risk her secret being revealed. She resolved to tough it out until after the exam, a fatal mistake and one Miara was anticipating. By the time she arrived at Selda's Kaeden's blood sugar had been raging out of control for days and was dangerously high. It would only take one large dose of sugar to finish her off.
When the police arrived at Selda's they approached a table with four communal bowls: milk, cream, artificial sweetener, and sugar. Miara waited until the others went to the jukebox, then hid the sugar and sweetener bowls in her purse, and left with the excuse of going to the bathroom. In the bathroom she poured the sugar into the sweetener bowl before returning it to the table. Kaeden had no idea she was adding sugar, not sweetener, to her coffee and her blood sugar reached lethal levels within minutes.
However it was the sugar swap which caused Miara to make a fatal mistake. With nothing to put the real sweetener into so that she could transfer it to the sugar bowl for an even swap, Miara was forced to discard the sweetener and hide the sugar bowl in her purse before returning the sweetener bowl filled with sugar to the table. Thus there was no sugar bowl on the table when Jho investigated, though the fugitives' table was supplied with one.
The fugitives presented their case to Ahsoka and a search of Miara's purse produced the sugar bowl and confirmation of Miara's guilt. Unfortunately for them the police had them come down to the station to take their statements, during which their prints were run. No one made it to Jamaica, though Ahsoka was impressed a slew of murderers had solved the case.