Calculating Maximum-Entropy Probability densities for Belief Functions

A common procedure for selecting a particular density from a given class of densities is to choose one with maximum entropy. The problem addressed here is this. Let S be a finite set and let B be a belief function on 2S. Then B induces a density on 2S, which in turn induces a host of densities on S. Provide an algorithm for choosing from this host of densities one with maximum entropy.