An unconvincing explanation of coincidences

Imagine you are being interrogated by police, after being arrested for a crime for which you are innocent but where there is circumstantial evidence strongly pointing to you. You calmly explain what happened, ending with

I know this looks highly suspicious but really it's just one of those amazing coincidences that happen sometimes.

Seeing a dubious look on the detective's face, you continue

Let me explain about coincidences (the following edited from Wikipedia Littlewood's law).

You stop talking. The detective stares at you for 10 seconds, then says

You have been found next to a dead body with a smoking gun. Your explanation involves a million hypothetical events you can't specify, none of which actually happened.
(To uniformed officer). Lock this guy up and get a psych evaluation!