The diffusion of an ion inside a charged planar slit micropore is analyzed from a stochastic point of view. Using the instantaneous relaxation approximation (IRA), the Fokker-Planck-Smoluchowski equation was used to calculate the survival probability ${G}_{i}(x,t),$ namely, the probability that an ion of species i remains inside the pore at time t given that it started to diffuse at a given position x. The ionic density profiles were obtained using the three-point extension hypernetted chain theory (HNC), which explicitly takes into account the finite ionic sizes, and the results are compared to those using the classical modified Gouy-Chapman (MGC) theory based on the Poisson-Boltzmann point-ion equation. Calculations were carried out for a variety of pore widths, electrolyte charges, surface potentials, and absorbing or reflecting boundary conditions. We also calculate the mean first passage time (MFPT), \ensuremath{\tau}, and the position-averaged MFPT, $\overline{\ensuremath{\tau}}.$ Our Smoluchowski HNC results show strong discrepancies with the classical Smoluchowski MGC theory. In particular, for small pores and doubly charge coions, we observed oscillations in the position-averaged MFPT, as a function of the pore size, which are absent in the classical theory.