Flash floods are recognized as a major threat to power distribution systems. Thus, enhancing distribution system resilience against this catastrophic natural hazard is essential and imperative. Commonly researchers have used two-dimensional (2D) surface flow models to evaluate flood risk on power systems. Though these 2D models can provide descriptions of overland flow propagation, they fail to provide overflow locations which are crucial in flash flood modelling. Furthermore, these models are computationally expensive, hence not suitable for real-time analysis. Therefore, this study presents a probabilistic flood model that is easy to develop and can handle heavy uncertainties related to urban flash flooding. In this respect, the Monte Carlo technique is employed to predict overflow locations in a grid-based environment. Considering rainfall intensity, soil moisture, and curvature of the surface, reinforcement learning is then leveraged to trace the flow path of floodwater from these overflow locations, to identify distribution substations at the risk of inundation. The proposed flood model is applied to IEEE 33-bus and a real 23-bus distribution systems considering a hypothetical terrain and validated on a real urban area. This work will assist decision-makers and utility operators in enhancing power system resiliency to urban flash floods while overcoming the barriers of limited data and time.