In 64 squares,
4 at-corner squares, each has only 2 options to select from so 4*2C1
6*4 = 24 side squares, each has only 3 options to select from so 24*3C1
6*6 = 36 inner squares , each has 4 options to select from so 36*4C1
So.
(4 * 2 + 24 *3 + 36* 4)/(64*63) = (224/4032) = 1/18