In Zuk et al. 2012, they claim:
The set of probability distributions on $m$ values is the $m-1$-dimensional simplex denoted $S_m$.
Probability distribution functions are familiar to me. I understand the basic notion of a simplex as a geometric object, and I recall them from how the simplex method can be geometrically interpreted as a traversal of simplex nodes. But I am not familiar with representing sets of probability distributions as a simplex.
How does this representation work?