"but all of these people live in the real world where accidents/sudden illness/etc do happen every day" Yes, but we can also use Bayesian methods. If someone w

"but all of these people live in the real world where accidents/sudden illness/etc do happen every day" Yes, but we can also use Bayesian methods. If someone with powerful, murderous enemies dies in an extremely improbable way, it's not statistically sound to just say "accidents happen every day". Of course you would need proof to actually convict someone, but it could definitely be a legitimate reason to start asking questions.