Multi-Object Tracking (MOT) aims to maintain stable and uninterrupted trajectories for each target. Most state-of-the-art approaches first detect objects in each frame and then implement data association between new detections and existing tracks using motion models and appearance similarities. Despite achieving satisfactory results, occlusion and crowds can easily lead to missing and distorted detections, followed by missing and false associations. In this paper, we first revisit the classic tracker DeepSORT, enhancing its robustness over crowds and occlusion significantly by placing greater trust in predictions when detections are unavailable or of low quality in crowded and occluded scenes. Specifically, we propose a new framework comprising of three lightweight and plug-and-play algorithms: the probability map, the prediction map, and the covariance adaptive Kalman filter. The probability map identifies whether undetected objects have genuinely disappeared from view (e.g., out of the image or entered a building) or are only temporarily undetected due to occlusion or other reasons. Trajectories of undetected targets that are still within the probability map are extended by state estimations directly. The prediction map determines whether an object is in a crowd, and we prioritize state estimations over observations when severe deformation of observations occurs, accomplished through the covariance adaptive Kalman filter. The proposed method, named MapTrack, achieves state-of-the-art results on popular multi-object tracking benchmarks such as MOT17 and MOT20. Despite its superior performance, our method remains simple, online, and real-time. The code will be open-sourced later.