Probabilistic reliability can overcome the shortage of traditional reliability index expectation which only measures system reliability from the mean perspective. However, with the expansion of distribution network scale and the surge of data volume, a probabilistic reliability calculation method that can balance calculation accuracy and calculation speed is urgently needed. Therefore, a fast calculation method for probabilistic reliability of distribution network based on Monte Carlo method is proposed. The improved three-point estimation method and the third-order polynomial normal transformation are used to effectively reduce the size of input sample points while retaining the correlation of input variables, and the probabilistic reliability is obtained by series expansion. Firstly, the improved three-point estimation method is used to select sample points in the independent standard normal space, which are then transformed into sample points in the original variable space through the third-order polynomial normal transformation. Then, the sequential Monte Carlo method is used to calculate the reliability of the sample points considering the island division. Finally, the probability distribution of reliability index is obtained through Edgeworth series expansion. The example analysis of the improved IEEE-RBTS Bus6 F4 feeder shows that there is only a maximum deviation of 2.195% between the reliability calculation results of the proposed method and the traditional Monte Carlo method, while the calculation time of the proposed method is only 1.05% of the traditional Monte Carlo method. It proves that the proposed method can significantly improve the calculation speed while ensuring high accuracy.