With the advent of large-scale electronic transportation, the construction of electric vehicle charging stations (EVCSs) has increased. The stochastic characteristic of the charging power of EVCSs leads to a risk of destabilization of the DC distribution network when there is a high degree of power electronification. Current deterministic stability analysis methods are too complicated to allow for brief descriptions of the effect of probabilistic characteristics of EVCSs on stability. This paper develops a probabilistic small-signal stability analysis method. Firstly, the probabilistic information of the system is obtained by combining the s-domain nodal impedance matrix based on the point estimation method. Then, the probability function of stability is fitted using the Cornish–Fisher expansion method. Finally, a comparison experiment using Monte Carlo simulation demonstrates that this method performs well in balancing accuracy and computational efficiency. The effects of line parameters and system control parameters on stability are investigated in the framework of probabilistic stability. This will provide a probabilistic perspective on the design of more complex power systems in the future.