No, for a qualitative change in various probabilities we can ask if Dumbledore has unpleasant associations with burning -- like a memory of something he wishes he didn't (have to) do, or of a sad time for his family. These would reduce the chance that he sees "setting fire to a chicken" as clever.

Seems like a sadistic DD who killed Narcissa would enjoy alluding to this event, in a way that would disturb Harry without making him suspect the purpose behind it. But that seems to me like a more complicated hypothesis than a Dumbledore who shares Donny's suspicions, given that DD looks like a 'bad guy' of a radically different kind.