It violates some intuition in me that no matter what particular outcome has occurred of a variable described by a continuous distribution, it must have had probability 0.
In Frequentist inference, I feel ok (but not great) by recognizing that the asymptotic value of the number of occurrences of any outcome divided by n (number of trials) is 0 as n approaches infinity.
In Bayesian, I don't feel satisfied (yet) with just saying that you can (correctly) have had 0 expectation of certainty for an outcome that has indeed happened.
I'm just hoping to find a perspective to understand this better.
Edit: Due to some confusion in the comments, I just want to emphasize that this is not a question about why point events must always have probability 0 in a (pure) continuous distribution. That is a strictly mathematical consequence because, for a given probability space, there cannot exist an uncountable number of disjoint events with probability greater than 0.
I'm just having trouble reconciling how we can interpret that with a Bayesian approach.