Due to the chaotic nature of the underlying physical processes, even state-of-the-art models cannot perfectly forecast the solar irradiance at the surface of the earth. There is, therefore, a growing interest in the research community for forecasting methods that can quantify their own uncertainty. This paper proposes a novel probabilistic framework for forecasting day-ahead hourly solar irradiance. A principal component analysis (PCA) is used to tightly combine a high-resolution mesoscale numerical weather prediction (NWP) model with a quantile gradient boosting algorithm. A thorough evaluation of the deterministic and probabilistic properties of the model is conducted for a full year in the tropical island of Singapore. The impact of the sky conditions on its performance is also considered. Furthermore, a rigorous statistical framework is employed to systematically benchmark our model against two state of the art methods, a Lasso model output statistic procedure and an analog ensemble (AnEn). Our model significantly improves the numerical weather prediction model: it achieves a 41% reduction of the MAE and 39% reduction of the RMSE. It is also slightly more accurate than Lasso and has a CRPS 4% lower than that of AnEn.