The way to make this analysis is to give the prior probabilities of your probability distribution, the posterior probabilities of your posterior probabilities are in order, and your posterior probabilities are exactly the same regardless of whether you have a credence that they are independent.
The way to make this analysis is to give the prior probabilities of your probability distribution, the posterior probabilities of your posterior probabilities are in order, and your posterior probabilities are exactly the same regardless of whether you have a credence that they are independent.