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.