We develop a probabilistic interpretation of two-stage object detection. We show that this probabilistic interpretation motivates a number of common empirical training practices. It also suggests changes to two-stage detection pipelines. Specifically, the first stage should infer proper object-vs-background likelihoods, which should then inform the overall score of the detector. A standard region proposal network (RPN) cannot infer this likelihood sufficiently well, but many one-stage detectors can. We show how to build a probabilistic two-stage detector from any state-of-the-art one-stage detector. The resulting detectors are faster and more accurate than both their one- and two-stage precursors. Our detector achieves 56.4 mAP on COCO test-dev with single-scale testing, outperforming all published results. Using a lightweight backbone, our detector achieves 49.2 mAP on COCO at 33 fps on a Titan Xp, outperforming the popular YOLOv4 model.