Important advances have been made in the methodologies for assessing the safety of dams, resulting in the review and modification of design guidelines. Many existing dams fail to meet these revised criteria, and structural rehabilitation to achieve the updated standards may be costly and difficult. To this end, probabilistic methods have emerged as a promising alternative and constitute the basis of more adequate procedures of design and assessment. However, such methods, in addition to being computationally expensive, can produce very different solutions, depending on the input parameters, which can greatly influence the final results. Addressing the existing challenges of these procedures to analyze the stability of concrete dams, this study proposes a probabilistic-based methodology for assessing the safety of dams under usual, unusual, and extreme loading conditions. The proposed procedure allows the analysis to be updated while avoiding unnecessary simulation runs by classifying the load cases according to the annual probability of exceedance and by using an efficient progressive sampling strategy. In addition, a variance-based global sensitivity analysis is performed to identify the parameters most affecting the dam stability, and the parameter ranges that meet the safety guidelines are formulated. It is observed that the proposed methodology is more robust, more computationally efficient, and more easily interpretable than conventional methods.