This paper describes a probabilistic Laplacian surface propagation (PLSP) framework for a robust stereo matching under severe radiometric variations. We discover that a progressive scheme overcomes an inherent limitation for this task, while most conventional efforts have been focusing on designing a robust cost function. We propose the ground control surfaces (GCSs) designed as progressive unit, which alleviates the problems of conventional progressive methods and superpixel based methods, simultaneously. Moreover, we introduce a novel confidence measure for stereo pairs taken under radiometric variations based on the probability of correspondences. Specifically, the PLSP estimates the GCSs from initial sparse disparity maps using a weighted least-square. The GCSs are then propagated on a superpixel graph with a surface confidence weighting. Experimental results show that the PLSP outperforms state-of-the-art robust cost function based methods and other propagation methods for the stereo matching under radiometric variations.