Known answer, missing proof inverts deduction
When the culprit's identity is revealed before any evidence is assembled, the puzzle shifts from 'who did it' to 'how can this be shown to someone who does not accept the source.' The detective has to work backward from a certain conclusion and build a chain of admissible, observable facts that reaches it. The revelation only counts once that chain exists, because testimony from a spirit persuades no court and no skeptic.