You are stating "I think ultra-intelligent machine will believe X", but this simply means that you believe X, so why the talk about ultra-intelligent machines? It serves no purpose.
(b) is counterfactual today. Nobody can calculate how many nearby star systems should have given birth to star faring civilizations - since nobody knows p(origin of life). We can't even make life from plausible inorganic materials yet. We are clueless - and thus highly uncertain.
Imagine that an ultra-intelligent machine emerges from an intelligence explosion. The AI (a) finds no trace of extraterrestrial intelligence, (b) calculates that many star systems should have given birth to star faring civilizations so mankind hasn’t pass through most of the Hanson/Grace great filter, and (c) realizes that with trivial effort it could immediately send out some self-replicating von Neumann machines that could make the galaxy more to its liking.
Based on my admittedly limited reasoning abilities and information set I would guess that the AI would conclude that the zoo hypothesis is probably the solution to the Fermi paradox and because stars don’t appear to have been “turned off” either free energy is not a limiting factor (so the Laws of Thermodynamics are incorrect) or we are being fooled into thinking that stars unnecessarily "waste” free energy (perhaps because we are in a computer simulation).