Large cryogenic pumps are installed in the vessel of large neutral beam injectors (NBIs) used to heat the plasma in nuclear fusion experiments. The operation of such pumps can be compromised by the presence of stray secondary electrons that are generated along the beam path. In this paper, we present a numerical model to analyze the propagation of the electrons inside the pump. The aim of the study is to quantify the power load on the active pump elements, via evaluation of the transmission probabilities across the domain of the pump. These are obtained starting from large datasets of particle trajectories, obtained by numerical means. The transmission probability of the electrons across the domain is calculated for the NBI of the ITER and for its prototype Megavolt ITer Injector and Concept Advancement (MITICA) and the results are discussed.