Hough transform based methods for detecting multiple objects use non-maxima suppression or mode-seeking to locate and distinguish peaks in Hough images. Such postprocessing requires tuning of many parameters and is often fragile, especially when objects are located spatially close to each other. In this paper, we develop a new probabilistic framework for object detection which is related to the Hough transform. It shares the simplicity and wide applicability of the Hough transform but at the same time, bypasses the problem of multiple peak identification in Hough images, and permits detection of multiple objects without invoking non-maximum suppression heuristics. Our experiments demonstrate that this method results in a significant improvement in detection accuracy both for the classical task of straight line detection and for a more modern category-level (pedestrian) detection problem.