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Would the output with the same conditional probability not also be the most likely in a conventional sense? I'm not understanding the distinction, but I'm not an expert so this might be a subtlety I just don't grasp

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Conditional probabilities are probabilistic. If you ask again you might get a different answer. The most likely answer is a single sample. It often isn't actually the result you want, it often has a much lower probability of occurring than your intuition would suggest, and even if it's correct once it's often not something you would appreciate appearing repeatedly if you re-asked the same question.

I can add more details/comparisons/nuance/explanations/... if you're curious why that matters, but hopefully the distinction is clear now?

I think that helped, thanks!

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