The vectorial capacity of a mosquito species that is a disease-vector indicates the expected number of infectious bites given by all mosquitoes infected from biting a single infected human individual, assuming perfect transmissions between humans and vectors. Assessing this number for different transmitting species of the same disease, such as dengue or malaria, expresses how capable these species are of spreading the disease. We describe the vectorial capacity as a random process and present a model for analyzing its probability distribution. Our stochastic model permits us to obtain the moment-generating function for the distribution of the vectorial capacity and, under reasonable assumptions, the probability distribution itself. A stochastic modeling framework is helpful for analyzing the dynamics of disease spreading, such as when performing sensitivity analysis.