Here's one challenge for your position. Take, for example, your first question. I don't think it makes any sense to talk about any probabilities there, since the question is incomplete to the point of meaninglessness. What sample of cars are we talking about, and under what exact circumstances? To which, I assume, you would answer that for everything unspecified, you should somehow make assumptions that are true with some probabilities and then use that to calculate the final probability of your answer, or estimate it just by feeling in some such way.

But how far would you take this principle? Suppose you receive this question in a bad handwriting, with one word totally smudged, so that it reads like "a [...] is white," or "a car is [...]." Would you be willing to assign a probability nevertheless, based on probabilistic guesses about the missing word? If yes, what about the case where two words are smudged, so the claim is "a [...] is [...]"? What about the ultimate case where the text is completely unreadable, so you have to guess what the question is?

(Note that we can arrive at your original question by starting with a well-defined problem with a computable exact answer, and then smudging parts of it so that we're left with "a car is white.")