High penetration of wind power into power grids deteriorates system frequency stability. Wind turbines (WTs) are required by grid codes to participate in primary frequency regulation (PFR) by adjusting their rotor speed to utilize the stored kinetic energy. However, frequency support causes a change in rotor speed, and hence, the PFR capability of a wind farm is limited by a time-varying boundary. As the mechanical transient process of the WT is determined by wind speed, it is necessary to forecast the PFR capability of wind farms based on wind speed distribution, to arrange the system scheduling plan while considering dynamic safety. In this paper, a physics-informed probability distribution assessment method is proposed for the PFR capability of wind farms considering wind speed uncertainty. Constructing the analytical correlation relationship between state variables based on Koopman-operator-theory-based state space transformation, the probability density function of the maximum feasible droop coefficient of a wind farm is derived based on the wind speed probability distribution. The simulation results demonstrate that the proposed method achieves a five-order-of-magnitude reduction in computational time compared with the Monte Carlo and time-domain simulation methods, and possesses the advantages of independence from physical parameters and random sampling errors, as well as a simple analytical expression of the probability distribution of PFR capability.