The study of the interplay between belief and probability has recently been posed in a geometric setup, in which belief functions are represented as points of a simplex called belief space. Each belief function b is associated with three different geometric entities, which in turn determine three different Bayesian function related to b. In this paper, in particular, we study the geometry of relative plausibilities, and show how equidistribution can be possibly a trait d'union among all the Bayesian relatives of a belief function.