Accurate hydrological drought prediction is crucial for disaster preparedness and sustainable water management, particularly in semi-arid regions where water scarcity presents critical challenges. Typically, many existing approaches often fail to adequately capture the inherent variability and interdependency of drought characteristics, reducing the reliability of risk assessments. As a solution, advanced probabilistic frameworks can aid in quantifying uncertainty and modelling complex dependencies among drought variables. To this end, the present study develops a Variational Bayesian Monte Carlo-based maximum entropy copula (VBMC-MEC) method to evaluate drought risk under uncertainty. The proposed approach enhances the fitting of drought variables (duration and severity) using the maximum entropy principle, effectively capturing inherent uncertainties and improves bivariate drought risk assessment through efficient posterior approximation. The VBMC-MEC method was applied to nine catchments of the Victorian sites of the Upper Murray Basin (UMB), Australia, which identified 70-109 drought events during 1955-2020, with average inter-arrival times of 6.94-7.73 months. The average drought durations ranged from 5.13 to 8.94 months, while drought severity values varied between 7.73 and 13.5, with the Millennium drought (2002-2009) being the most severe. Moreover, VBMC demonstrated superior performance compared to Markov Chain Monte Carlo (MCMC) on high-dimensional datasets, while posterior distributions of copula parameters from VBMC were found to be similar to those obtained from MCMC. The results further showed that the hydrological drought index (HDI) at a 1-month time scale (HDI-1) is more suitable for predicting drought frequency at 5- and 10-year return periods, whereas HDI-3 and HDI-6 better capture drought risks for longer return periods (20-, 50-, and 100-year). Consequently, the joint return period may be used as the upper limit for the target return period, while the lower limit can be defined when either the duration or severity surpasses the drought threshold. Overall, the findings of this research establish a solid foundation for effective drought risk assessment, which can be helpful in more accurate and effective drought prevention and management decisions under evolving hydroclimatic conditions.