To improve the energy system resilience and economic efficiency, the wind power as a renewable energy starts to be deeply integrated into smart power grids. However, the wind power forecast uncertainty brings operational challenges. In order to provide a reliable guidance on operational decisions, in this paper, we propose a short-term wind power probabilistic forecast. Specifically, to model the rich dynamic behaviors of underlying physical wind power stochastic process occurring in various meteorological conditions, we first introduce an infinite Markov switching autoregressive model. This nonparametric time series model can capture the important properties in the real world data to improve the prediction accuracy. Then, given finite historical data, the posterior distribution of flexible forecast model can correctly quantify the model estimation uncertainty. Built on it, we develop the posterior predictive distribution to rigorously quantify the overall forecasting uncertainty accounting for both inherent stochastic uncertainty and model estimation error. Furthermore, the proposed approach can provide accurate and reliable short-term wind power probabilistic forecast, which can be used to support smart power grids real-time risk management.