"Yes, there are some unusual patterns to these - her patients, but we have nothing to prove anything other than statistical anomalies."
A vicious murder happens in a town that the party happens to pop in at. Under heavy suspicion as they are strangers, the party is forced to discover the perpetrator or have their reputations blackened, especially as more and more murders occur in the town, and mysteriously stop and restart when the party leaves to go kill off that evil necromancer who kidnapped the princess.
The only problem is that a demon, possessing one of the party, is the perpetrator. And the demon makes no signs that its living in the PC's head.
In fact, for all the party knows (except for the possessed person's), their companion is an evil murderer.
Do they try and execute their friend as he's a vicious murderer, and no evidence points to demonic posession? Or do they flee town with him, trusting him, and have their reputations destroyed?