The more leads Dumbledore pursues that turn out to be false, the less likely it will seem that any future lead is true.
Kind of like how “Santa Clause” told Harry that Dumbledore would take away his cloak, so that when Dumbledore didn’t, Harry trusted him more than before the suspicion.
Except he wants to give the impression that he doesn’t know anything about the body’s disappearance and it’s entirely someone else’s work.
The more leads Dumbledore pursues that turn out to be false, the less likely it will seem that any future lead is true.
Kind of like how “Santa Clause” told Harry that Dumbledore would take away his cloak, so that when Dumbledore didn’t, Harry trusted him more than before the suspicion.