Noting that the input data to my histogram block is not necessarily a population, it may just be sampled from one.  In that case the expression I wrote earlier is not strictly true.

When you sample from something, the distribution described by the different samplings is normal.  So the probability of the true population measure being any particular thing, is the same as the probability of a normal distribution having a particular mean, given one of its values and it's standard deviation.

Finding that answer means knowing the distribution of possible probability distributions, without regard to the sample.  I think if we assume a uniform distribution of actual histograms possible in all reality, then the distribution of values of a single bin would be a function of that uniform distribution of histograms, and which bin it is ...  that's not quite uniform, as the number of options the rest of a histogram has changes depending on the density used by a bin, but it's probably some drivable algebraic expression.  Simulating is always good to test things.