Autonomous vehicles must navigate dynamically uncertain environments while balancing safety and efficiency. This challenge is exacerbated by unpredictable human-driven vehicle (HV) behaviors and perception inaccuracies, necessitating planners that adapt to evolving uncertainties while maintaining safe trajectories. Overly conservative planning degrades driving efficiency, while deterministic methods risk failure in unexpected scenarios. To address these issues, we propose a real-time contingency trajectory optimization framework. Our method employs event-triggered online learning of HV control-intent sets to dynamically quantify multimodal HV uncertainties and incrementally refine their forward reachable sets (FRSs). Crucially, we enforce invariant safety through FRS-based barrier constraints that ensure safety without reliance on accurate trajectory prediction. These constraints are seamlessly embedded in contingency trajectory optimization and solved efficiently through consensus alternating direction method of multipliers (ADMM). The system continuously adapts to HV behavioral uncertainties, preserving feasibility and safety without excessive conservatism. High-fidelity simulations on highway and urban scenarios, along with a series of real-world experiments, demonstrate significant improvements in driving efficiency and passenger comfort while maintaining safety under uncertainty. The project page is available at https://pathetiue.github.io/frscp.github.io/.