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.<xref ref-type="bibr" rid="bibr1-0954410012467725">¹</xref> 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.<xref ref-type="bibr" rid="bibr2-0954410012467725">²</xref> We advocate the adaptive splitting technique, presented in Cérou et al.,<xref ref-type="bibr" rid="bibr3-0954410012467725">³</xref> 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.