Probability of drawing an ace or 2 after an ace

Question

From a standard 52 card deck, we draw one card at a time without replacement. After having drawn the first ace, the game continues until either

1. We draw another ace, or
2. We draw a 2,

and the game then stop. Which events of the two is more likely, and what are the corresponding probabilities?

Edit: It is not very hard to get the probability = 0.5 with calculations. but can we come up with some more intuitive explanations?