Probabilistic solar power forecasting plays an important role in solar power grid integration and power system operations. One of the most popular probabilistic solar forecasting methods is to feed simulated explanatory weather scenarios into a deterministic forecasting model. However, the correlation among different explanatory weather variables are seldom considered during the scenario generation process. This paper presents an improved probabilistic solar power forecasting framework based on correlated weather scenario generation. Copula is used to model a multivariate joint distribution between predicted weather variables and observed weather variables. Massive weather scenarios are obtained by deriving a conditional probability density function given a current weather prediction by using the Bayesian theory. The generated weather scenarios are used as input variables to a machine learning-based multi-model solar power forecasting model, where probabilistic solar power forecasts are obtained. The effectiveness of the proposed probabilistic solar power forecasting framework is validated by using seven solar farms from the 2000-bus synthetic grid system in Texas. Numerical results of case studies at the seven sites show that the developed probabilistic solar power forecasting methodology has improved the pinball loss metric score by up to 140% compared to benchmark models.