This does not include putting the card back into the deck after it has been drawn.
I am comfortable with the number of ways two draw any two cards in a row (basic permutation of $52!/(52-2)!=52\times 51$.
I am also comfortable with the number of ways to draw any two spades in a row: $13!/(13-2)!=13\times12$ since there are 13 spades to choose from.
However, I am finding it hard to visualise and compute the way in which any card other than a spade is drawn, followed by a spade.
I think the correct answer is $39\times13=637$ from basic observation. (I.e. if there only existed 1 spade and 39 other cards then the number of permutations is 39, so with 13 spades the number of permutations is multiplied by 13.) But I want to do this in terms of well-defined permutation/combinatoric maths.