A post-biological flying machine is purely speculative science-fiction at this point, there is not a single real example that we can point to yet. This might one day change if we become a post-biological flying civilization, but so far not a single example of such has ever been seen.
Suppose the year is 1770 and I am a sailor on one of Captain Cook's expeditions. A fellow sailor breathlessly tells me about the advanced civilizations with flying machines we might encounter, reasoning that such constructions are theoretically possible according to science and extrapolating from extant technology. I'd tell him that I expect nothing of the sort.
I'd also concede that such technology might one day be created: " This might one day change if we become a post-biological civilization, but so far not a single example of such has ever been seen."
So far? No evidence for it. So far, it's only science fiction.
But I think that you are using correctly your likelihoods but forgetting your priors. The prior in this case is: there is no reason that we know for this not to happen, so, it has to be happening somewhere.
Post-biological life: There is presently no evidence of it happening even once.