For monocular RGB-based 3D pose and shape estimation, multiple solutions are often feasible due to factors like occlusion and truncation. This work presents a multi-hypothesis probabilistic framework by optimizing the Kullback-Leibler divergence (KLD) between the data and model distribution. Our formulation reveals a connection between the pose entropy and diversity in the multiple hypotheses that has been neglected by previous works. For a comprehensive evaluation, besides the best hypothesis (BH) metric, we factor in visibility for evaluating diversity. Additionally, our framework is label-friendly, in that it can be learned from only partial 2D keypoints, e.g., those that are visible. Experiments on both ambiguous and real-world benchmarks demonstrate that our method outperforms other state-of-the-art multi-hypothesis methods in a comprehensive evaluation. The project page is at https://gloryyrolg.github.io/MHEntropy.