Risk assessment is a crucial component of collision warning and avoidance systems in intelligent vehicles. To accurately detect potential vehicle collisions, reachability-based formal approaches have been developed to ensure driving safety, but suffer from over-conservatism, potentially leading to false-positive risk events in complicated real-world applications. In this work, we combine two reachability analysis techniques, i.e., backward reachable set (BRS) and stochastic forward reachable set (FRS), and propose an integrated probabilistic collision detection framework in highway driving. Within the framework, we can firstly use a BRS to formally check whether a two-vehicle interaction is safe; otherwise, a prediction-based stochastic FRS is employed to estimate a collision probability at each future time step. In doing so, the framework can not only identify non-risky events with guaranteed safety, but also provide accurate collision risk estimation in safety-critical events. To construct the stochastic FRS, we develop a neural network-based acceleration model for surrounding vehicles, and further incorporate confidence-aware dynamic belief to improve the prediction accuracy. Extensive experiments are conducted to validate the performance of the acceleration prediction model based on naturalistic highway driving data, and the efficiency and effectiveness of the framework with the infused confidence belief are tested both in naturalistic and simulated highway scenarios. The proposed risk assessment framework is promising in real-world applications.