Abstract: The NRL Pump protocol defines a multilevel secure component whose goal is to minimize leaks of information from high level systems to lower level systems, without degrading average time performances. We define a probabilistic model for the NRL Pump and show how a probabilistic model checker (FHP-mur$\varphi$) can be used to estimate the capacity of a probabilistic covert channel in the NRL Pump. We are able to compute the probability of a security violation as a function of time for various configurations of the system parameters (e.g. buffer sizes, moving average size, etc). Because of the model complexity, our results cannot be obtained using an analytical approach and, because of the low probabilities involved, it can be hard to obtain them using a simulator.