Probability density function of the escape probability (H I, Ca II, and Mg II) as a function of the column density of the specific ion. Colored lines show relations from the recipe of CL12 (red) and the adopted fit of the PDF (yellow). We note that in the middle and right panels, the results are plotted as a function of column density of Ca II and Mg II, respectively, and thus we do not plot the results from the recipe of CL12.