This study introduces a new, more advanced statistical approach to better capture these uncertainties in how water level relates to river flow. By using a sophisticated statistical framework and real-world river measurements, we've developed probabilistic rating curves that show a range of possible water level and flow combinations, rather than just one fixed value. We then integrated these probabilistic relationships with flood mapping technology to create probabilistic flood inundation maps. These maps provide a more comprehensive picture of potential flood extents, offering a wider range of scenarios than conventional methods. This work highlights that considering the inherent uncertainty in natural systems, like rivers, leads to more realistic and useful flood predictions. Ultimately, these improved predictions of flood extent can help guide better flood response strategies and emergency action plans.