In this paper, we present a novel probabilistic compact representation of the on-road environment, i.e., the dynamic probabilistic drivability map (DPDM), and demonstrate its utility for predictive lane change and merge (LCM) driver assistance during highway and urban driving. The DPDM is a flexible representation and readily accepts data from a variety of sensor modalities to represent the on-road environment as a spatially coded data structure, encapsulating spatial, dynamic, and legal information. Using the DPDM, we develop a general predictive system for LCMs. We formulate the LCM assistance system to solve for the minimum-cost solution to merge or change lanes, which is solved efficiently using dynamic programming over the DPDM. Based on the DPDM, the LCM system recommends the required acceleration and timing to safely merge or change lanes with minimum cost. System performance has been extensively validated using real-world on-road data, including urban driving, on-ramp merges, and both dense and free-flow highway conditions.