In modern intelligent transport systems, optimizing path selection in stochastic road networks has become crucial for autonomous vehicles and mobility on demand services. The unpredictability of travel times, due to factors like traffic congestion and weather conditions, necessitates a probabilistic approach to optimum path finding routing. This paper proposes an optimal stochastic routing algorithm that balances travel time and probability distribution in road networks where each road segment has uncertain travel times. We model the road network as a directed graph, with each edge representing a road segment characterized by multiple possible travel times and their associated probabilities. The algorithm identifies the shortest time path, a path with the highest probability of reaching the destination, and a trade-off path that balances travel time and the probability of reaching the destination. Simulation results on a Manhattan-like grid network demonstrate that the proposed method effectively reduces the risk of delays while maintaining reasonable travel times, thereby offering a practical solution for real-time path finding in uncertain traffic conditions.