Multiple extended target tracking (ETT) has gained increasing attention due to the development of high-precision LiDAR and radar sensors in automotive applications. For LiDAR point cloud-based vehicle tracking, this paper presents a probabilistic measurement-region association (PMRA) ETT model, which can describe the complex measurement distribution by partitioning the target extent into different regions. The PMRA model overcomes the drawbacks of previous data-region association (DRA) models by eliminating the approximation error of constrained estimation and using continuous integrals to more reliably calculate the association probabilities. Furthermore, the PMRA model is integrated with the Poisson multi-Bernoulli mixture (PMBM) filter for tracking multiple vehicles. Simulation results illustrate the superior estimation accuracy of the proposed PMRA-PMBM filter in terms of both the positions and extents of vehicles compared with PMBM filters using the gamma Gaussian inverse Wishart and DRA implementations.