what principles allow us to say that P!=NP is more likely to be true than false

Maybe we use the same principle that allows me to say "I guess I left my wallet at home" after I fail to find the wallet in the most likely places it could be, like my pockets. In other words, maybe we do Bayesian updating about the location of the "true" proof or disproof, as we check some apriori likely locations (attempted proofs and disproofs) and fail to find it there. This idea is still very vague, but looks promising to me because it doesn't assume logical omniscience, unlike Abram's and Benja's ideas...