Initial example: Ace, Jack, and King. What is the probability the Ace will be drawn before the Jack?
Answer: 50/50
Reason: 6 possibilities (3!), 3 where Ace is drawn before, 3 where Ace is drawn after the Jack.
How to generalize this example for N cards? I'm having trouble wrapping my head around this. Is it always 50/50?
Yes, the probability will always be $50$-$50$. There's a $1$-$1$ correspondence between permutations where the Ace precedes the Jack and permutations where the Jack precedes the Ace, obtained by simply taking a given permutation and reversing the Jack and the Ace. Moreover, those two possibilities exhaust all of the possible permutations. So the Ace will always precede the Jack in exactly half of the possible permutations.