Oh, and to talk about "the probability that John F. Kennedy was shot, given that Lee Harvey Oswald didn't shoot him", we write:

P(Kennedy_shot|Oswald_not)

If I've understood you, this is supposed to be a high value near 1. I'm just a noob at Bayesian analysis or Bayesian anything, so this was confusing me until I realised I also had to include all the other information I know: i.e. all the reports I've heard that Kennedy actually was shot, that someone else became president, and so on.

It seems like this would be a case where it's genuinely helpful to include that background information:

P(Kennedy_shot | Oswald_not & Reports_of_Kennedy_shot) = 1 or thereabouts

And to talk about "the probability that John F. Kennedy would have been shot, if Lee Harvey Oswald hadn't shot him", we write:

P(Oswald_not []-> Kennedy_shot)

Presumably this is the case where we pretend that all that background knowledge has been discarded?

P(Kennedy_shot | Oswald_not & no_knowledge_of_anything_after_October_1963) = 0.05 or something?