In modern-day power grids, increasing participation of inverter-based generation (i.e., wind/solar generation) increases supply uncertainty, reduces grid inertia, and exacerbates security-related problems. This article develops a stochastic framework to assess the grid's ability to withstand generator failure, while explicitly considering the supply and demand uncertainty. The framework enables proactive risk quantification and management to support secure operation of the modern-day power grid. It also allows consideration of adverse event probability after a generator failure to assess the relative importance of generator failure events. We demonstrate the proposed framework using a 200-bus synthetic grid. We find that probabilistic assessment is able to identify important contingencies, which would have been missed by deterministic analyses performed using mean values. We also develop a method for identifying important generator contingencies based on the probabilistic security and reliability analyses. We find that the resulting importance ranking is not identical to the generator capacity-based ranking and depends on the uncertainty in the generator's active power output as well as its contribution to grid inertia.