Groundwater sustains human activity in arid crystalline terrains where surface water is scarce and hydrogeological data are limited. However, most groundwater potential mapping approaches depend on deterministic weighting methods without quantifying model variability. This study describes an uncertainty-aware Remote Sensing and Geographic Information Systems (RS–GIS) framework to delineate groundwater potential zones in the Wadi Arab Watershed, Northeastern Sudan. Nine thematic factors—geology and lithology, rainfall, slope, drainage density, lineament density, soil, land use/land cover, topographic wetness index, and height above nearest drainage—were integrated using the Analytical Hierarchy Process (AHP), with acceptable consistency (Consistency Ratio (CR) < 0.1). To address subjectivity in weights, a Dirichlet-based Monte Carlo simulation (500 iterations) was implemented to perturb AHP weights whilst preserving compositional constraints. The resulting Groundwater Potential Index (GWPI) classified 32.69% of the watershed as high to very high potential, primarily associated with alluvial deposits and fractured crystalline rocks. Model validation using Receiver Operating Characteristic (ROC) analysis yielded an Area Under the Curve (AUC) of 0.704, indicating acceptable predictive performance. Uncertainty assessment showed low spatial variability (mean standard deviation (SD) = 0.215) and stable exceedance probabilities, verifying the robustness of predicted high-potential zones. The proposed probabilistic AHP framework augments decision reliability and provides a transferable, cost-effective tool for groundwater planning in data-limited arid basement environments.