Older models of Galactic chemical evolution (GCE) predict [K/Fe] ratios as much as 1dex lower than those inferred from stellar observations. Abundances of potassium are mainly based on analyses of the 7698{AA} resonance line, and the discrepancy between GCE models and observations is in part caused by the assumption of local thermodynamic equilibrium (LTE) in spectroscopic analyses. We study the statistical equilibrium of KI, focusing on the non-LTE effects on the 7698{AA} line. We aim to determine how non-LTE abundances of potassium can improve the analysis of its chemical evolution, and help to constrain the yields of GCE models. We construct a new model KI atom that employs the most up-to-date atomic data. In particular, we calculate and present inelastic e+K collisional excitation cross-sections from the convergent close-coupling (CCC) and the B-Spline R-matrix (BSR) methods, and H+K collisions from the two-electron model (LCAO). We constructed a fine, extended grid of non-LTE abundance corrections based on 1D MARCS models that span 4000<Teff/=K<8000, 0.50<logg<5.00, -5.00<[Fe/H]<+0.50, and applied the corrections to potassium abundances extracted from the literature.