Droughts, one of the most destructive natural hazards, are profoundly affected by climate change, which alters the hydrological cycle and influences drought propagation dynamics. This study investigates how changing climate may affect drought propagation by analyzing the probability of meteorological droughts evolving into agricultural and hydrological droughts. We utilized a probabilistic Bayesian model across 464 CAMELS (Catchment Attributes and Meteorology for Large-Sample Studies) basins across the contiguous United States. Each basin was simulated using the pre-calibrated Community Land Model Version 5 (CLM5), which models hydrological processes under both historical and projected future climates. To account for the uncertainties of future climates, we used the recently developed WRF-TGW dataset, where the Weather Research and Forecasting (WRF) model dynamically downscales climate reanalysis and future climate projections were developed using a thermodynamic global warming (TGW) approach. This approach replays historical weather events under a range of warming scenarios derived from CMIP6 climate scenarios and GCM models. We applied a drought matching technique, based on propagation times, to establish the causal pathways between different types of droughts. By employing a Bayesian conditional probability model on these paired drought events, we quantified the likelihood that meteorological droughts would lead to agricultural and hydrological droughts under different TGW scenarios. By investigating and quantifying the shifts in drought propagation probabilities, this study can aid in early drought warning systems and mitigation efforts and provides a robust risk assessment framework for decision-making in the face of a changing climate.