What is the probability that two squares(smallest dimension) selected randomly from a chess board have only one common corner?

There are 36 interior squares on a chess board. All these have 4 corners. So, a pair of squares having a common corner can be selected from these in 36*4 ways.
There are 24 squares on the border (excluding the corners). These have two corners each. So, the number of ways of selecting a pair of squares from these is 24*2.
There are 4 corner squares which have only 1 corner each (facing the chess board). So, the number of ways of selecting a pair of squares is 4 * 1.

So, numerator = (36 * 4 + 24 * 2 + 4 * 1) / 2 (it should be divided by 2 to take care of repetitions - each pair of squares in the aboe list is selected twice)
Denominator = $$^{64}C_2$$

So, required probability = $$\frac{7}{144}$$