I will roll a dice, and ask you, what is your probability of guessing the roll at random. The answer is 1/6, obviously. Then I will look at the result, and tell you, if the answer is 5 or not. What is the probability that you will guess the number right afterwards?
In Bayesian, you can encode the extra info into the prior, saying that the prior p = 1/5 if result is not 5, and 0 otherwise. Then the posterior being the normalized product between normal dice roll and the prior will be the same as the prior, which makes sense, you should have 1/5 chance to guess the dice correctly, if, for example, you know it is not 5.
Are there other ways of solving this problem. In particular, I am looking for a formal frequentist solution.