Any prediction of the future position and trajectory of an aircraft will contain errors due to both uncertainty caused by the environment and imperfect and incomplete information available to the prediction system. These prediction errors complicate conflict detection and resolution resulting in late or missed conflict detections and false alerts. Generally there are two types of conflict detection systems: geometric and probabilistic, and both of these systems have techniques for dealing with errors. These techniques often involve setting spatial buffers and limited time horizons, but these buffers are often not easy to select for optimized performance for specific trajectory prediction systems. This paper presents a probabilistic conflict detection system that uses a characterization of the trajectory prediction errors as input to minimize missed and false alerts instead of using derived buffers. The extra information provided by the probabilistic detector over a geometric detector can also be used by automated conflict resolution systems to pick more robust resolutions; balancing extra delay over reduced probability of recurrence of the conflict. Conflict detection results show that the probabilistic system can reduce missed alerts by about 10% while maintaining the same false-alert rate or reduce false alerts by about 25% while maintaining the same missed-alert rate when compared to a simple geometric system. When combined with a conflict resolution system, the probabilistic detection system provides more robust resolutions, reducing the number of resolutions required by about one third, but these resolutions require nearly twice as much total delay as the resolutions selected using a geometric detection system.