> No, it doesn't. A continuous distribution is just a way of assigning probabilities to a parameterized set of propositions where the parameters are continuous and so the set is infinite. But for any given proposition in that set the prior is a number.
A continuous distribution does not assign probabilities to each proposition but subsets of them. To see this concretely consider the continuous Uniform distribution from 1 to 1.5. It will for all values of its support have a probability density of 2. Most people would not consider 2 a probability.
For continuous distributions, Bayes's theorem becomes about probability densities and not probabilities.
A continuous distribution does not assign probabilities to each proposition but subsets of them. To see this concretely consider the continuous Uniform distribution from 1 to 1.5. It will for all values of its support have a probability density of 2. Most people would not consider 2 a probability.
For continuous distributions, Bayes's theorem becomes about probability densities and not probabilities.