Soft open point (SOP) is an important equipment to improve the flexibility of distribution networks. Conventional fault reconfiguration methods assume determinant values for loads and distributed generator outputs, which may lead to a reconfiguration solution that cannot satisfy operational constraints of distribution networks. This paper proposes a fault reconfiguration method for distribution networks with SOPs considering the uncertainties of photovoltaics and loads. Firstly, a fast probabilistic power flow method based on voltage sensitivity for distribution networks with SOPs is proposed. Secondly, the fault reconfiguration model considering uncertainties of photovoltaics and load is formulated to minimize load shedding and network losses. A genetic algorithm is adopted to solve the model. Finally, simulations on the 33-bus and 69-bus distribution systems are given to verify the effectiveness of the proposed method.