Collision between satellites and debris is a rare event but with high financial consequences. This risk therefore has to be addressed carefully. To support the decision to start a collision avoidance maneuver, a dedicated tool to characterize the risk uncertainty is the probability of collision between the debris and the satellite. Crude Monte Carlo could be a way if it could cope with very small probabilities, say 10^-6, within the available simulation budget and time. The methodology nowadays in use is a numerical integration made tractable by physical hypothesis and numerical approximation. We advocate the adaptive splitting technique, presented in Cérou et al. (2007), as it avoids all the hypothesis needed for the numerical integration and clearly outperforms Crude Monte Carlo with respect to rare events. A direct comparison between Crude Monte Carlo and adaptive splitting technique approach is also given on real-life examples.