Not sure how math/logic factors into this for you but the impossibility of proving a negative seems to apply here. It's one of the basic bits of logic I teach patients (at least when they ask about reality testing, which is rare). I tell them it's pretty near impossible to prove something doesn't exist or didn't happen, and that I find the best thing is to focus on what was most likely. It's very rare I don't find a very mundane reason for pretty much everything, and the few things I can't there's pretty much nothing I can do about anyway.