We present an approach and relevant models for predicting the probabilistic shock-to-detonation transition (SDT) behavior and Pop plot (PP) of heterogeneous energetic materials (HEM) via mesoscopic microstructure-explicit (ME) and void explicit (VE) simulations at the millimeter (mm) sample size scale. Although the framework here is general, the particular material considered in this paper is pressed Octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine (HMX). To systematically delineate the effects of material heterogeneities, four material cases are considered. These cases are homogeneous material, material with granular microstructure but no voids, homogeneous material with voids, and material with both granular microstructure and voids. Statistically equivalent microstructure sample sets (SEMSS) are generated and used. Eulerian hydrocode simulations explicitly resolve the material heterogeneities, voids, and the coupled mechanical-thermal-chemical processes. In particular, it is found that both microstructure and voids strongly influence the SDT behavior and PP. The effects of different combinations of microstructure heterogeneity and voids on the SDT process and PP are quantified and rank-ordered. The overall framework uses the Mie-Gruneisen equation of state and a history variable reactive burn model (HVRB). A novel probabilistic representation for quantifying the PP is developed, allowing the calculation of (1) the probability of observing SDT at a given combination of shock pressure and run distance, (2) the run-distance to detonation under a given combination of shock pressure and prescribed probability, and (3) the shock pressure required for achieving SDT at a given run distance with a prescribed probability. The results are in agreement with general trends in experimental data in the literature.