> There are many possible world destroying events that don't involve AI. And AI could solve them.

The entire subset of them that has humans as a cause of doom is automatically in the set of AI-doom scenarios, because AI can directly or indirectly operate anything humans can.

What's the time cutoff for the question? Based on most current mainstream understanding of physics (ex. https://en.wikipedia.org/wiki/Timeline_of_the_far_future), and mainstream understanding of "doom", at unbounded time horizons P(doom)=1 (and hence also both conditionals, as long as you accept 0<P(AI)<1).