Flies and Smoke
A guard looks out into the distance, and sees a black cloud. “Ah, smoke!” he thinks, “There’s a fire there.”. He remarks as much to his friend, who, slightly more eagle-eyed, identifies the cloud as flies. “Ah,” he thinks, “Then there is not a fire there after all.”
This is based on Dharmottara’s commentary on Dharmakirti’s Ascertainment of Knowledge, which questions the “justified true belief” theory of knowledge (the initial consideration of a fire being justified and true, yet backed up with the wrong evidence).
I continue it to reference a different mistake: initially, the evidence for the presence of a fire was the presence of smoke. After the smoke was revealed to be flies, the guard counts that as evidence against there being a fire. However, this should merely bring the chance down to the chance of there being a fire anywhere: it doesn’t make the area particularly unlikely to have a fire.
This is a form of denying the antecedent. Here, removing evidence in favour of a proposition is counted as providing evidence against it.