The increasing interest in integrating volatile resources into microgrids implies the necessity of quantifying the uncertainty of photovoltaic (PV) production using dedicated probabilistic forecast techniques. The work presents a novel method to construct ultra-short-term and short-term prediction intervals (PIs) for solar global horizontal irradiance (GHI). The model applies the k-means algorithm to cluster observations of the clear-sky index according to the value of selected data features. At each timestep, the features are compared with the actual conditions to identify the representative cluster. The lower and upper bounds of the PI are calculated as the quantiles of the irradiance instances belonging to the selected cluster at a target confidence level. The validation is performed in 3 datasets of GHI measurements, each one of 85 days. The model is able to deliver high performance PIs for forecast horizons ranging from sub-second to intra-hour ahead without the need of additional sensing systems such as all-sky cameras.