The Strait of Istanbul is one of the world's busiest, narrowest and most winding waterways. As such, there is a high grounding probability for vessels. Although a number of grounding probability models exist, they have been deemed unsuitable by local maritime experts, due to their insufficient stopping distance criteria for narrow waterways. Thus, there is a need for a new model. This paper proposes a two-component grounding probability model that multiplies the geometric grounding probability (calculated with a kinematic-based model) with the causation probability (calculated with a specially designed Bayesian network). The geometric probability model is improved in terms of stopping distance parameters and the Bayesian network is crafted for narrow waterways. The model is then deployed with pre-determined parameters within the Strait of Istanbul to run risk analysis scenarios. The results, validated with actual grounding records, show that the causation probability is the key component for quantifying the probability of grounding in narrow waterways. If navigated without frequent evasive manoeuvres, grounding would be almost inevitable. Although this study focuses on the Strait of Istanbul, the proposed approach can be applied to research into grounding probability of vessels navigating through other waterways.