In the recent past, the Gravity Recovery and Climate Experiment (GRACE) satellite mission and its successor GRACE Follow-On (GRACE-FO), have become invaluable tools for characterizing drought through measurements of Total Water Storage Anomaly (TWSA). However, the existing approaches have often overlooked the uncertainties in TWSA that stem from GRACE orbit configuration, background models, and intrinsic data errors. Here we introduce a fresh view on this problem which incorporates the uncertainties in the data: the Probabilistic Storage-based Drought Index (PSDI). Our method leverages Monte Carlo simulations to yield realistic realizations of the stochastic process of the TWSA time series. These realizations depict a range of plausible drought scenarios that later on are used to characterize drought. This approach provides probability for each drought category instead of selecting a single final category at each epoch. Since the GRACE record is short (less than 20 years), we have hindcasted the TWSA back to 1980. To this end, we have used a combination of three different groups of models, namely Land Surface Models (LSMs), Global Hydrological Models (GHMs), and global atmospheric reanalysis models to estimate TWSA for the pre-GRACE era, back to 1980. To combine models, we have used the Multivariate Linear Regression (MLR) method.