From Computational Statistics (CSE383M and CS395T)
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Parameters: Random variables that are associated with the probability we're trying to solve for. The parameters themselves can be either continuous or discrete. For example, in the Jailer's Tip scenario, the probability that the jailer "says B" given that B and C are going to be released is represented by a parameter labeled x. This parameter belongs to a continuous distribution, taking values between 0 and 1. P(x) depends on the background information that is available to the prisoner and thus P(x) is defined as the conditional probability P(x|I). Assuming that the jailer doesn't have a preference for either B or C, x is assigned a dirac delta distribution with its mass concentrated at 1/2.Depending on what distribution x is taken from, P(A|S_b) changes. The reason p(x) is called a "probability of a probability" is because it is the probability that the P(A|S_b) takes on a specific value, which in itself is a probability.