A lattice gas model is used with Wang-Landau Monte Carlo sampling to predict the capillary force between a model of an atomic force microscopy (AFM) probe and a smooth surface as a function of separation, relative humidity (RH), and tip hydrophilicity. Completely wetting AFM tips exhibit a maximum in the capillary force as the RH increases, while the magnitude of the capillary force in the presence of partially wetting and partially drying tips is relatively independent of the RH. Capillary forces can also be significant in low RH environments and should not be discounted in AFM studies involving hydrophilic surfaces.