In this paper, we address aircraft conflict detection on a mid-term horizon. We adopt a probabilistic approach and provide a simple method to estimate the probability of two aircraft getting closer than some minimum predefined distance, based on a commonly adopted Gaussian model of the deviation from their planned trajectories. A key feature of our method is that the probability estimate is accompanied by a deterministic accuracy certificate. This is achieved by adopting a geometric approach to conflict probability estimation and jointly computing a lower and an upper bound on the conflict probability. These bounds can be inspected and refined if the resulting accuracy of the probability estimate is not adequate. Successive refinements are guaranteed to lead to an estimate with the desired accuracy. Numerical results show the effectiveness of the proposed method.