What is the Probability that a Knight stays on chessboard after N hops?

What is the Probability that a Knight stays on chessboard after N hops?

Say a 8x8 chessboard as per picture.

A position is represented here by co-ordinates(x,y).
A move is aslo considered as valid, where the Knight lands outside the
chessboard [ For eg. from (3,2) towards (3,1) but ends up outside
chess-board. ]
But once outside, it can't come back.
Question:
Knight starts from (0,0). What is the Probability that a Knight stays on
chessboard after N hops?
Expected Solution:
I don't want exact result like $ \frac{12}{64} $ but need your help on
a. the thought/procedure/methodology to find it with
b. A concluding formulae in terms of permutation/combination,
I have thought something which I don't want to disclose here in order to
avoid others to be confused and biased by my thought. Spare me for that.