I don't understand where does the $\frac{k-1}{k}$ factor come from, in the probability mass function derived by Bayesian approach.

Question

I don't understand where does the $\frac{k-1}{k}$ factor come from, in the probability mass function derived by Bayesian approach:

https://en.wikipedia.org/wiki/German_tank_problem

(in the Example section, near the top of the article)

Answer 1

It's derived later on in the same article, in the "Summation Formula" subsection.