Standard deck of 52 cards

Hello, I'm not sure how to set this up. Any help would be greatly appreciated. Thank you.

Standard deck of 52 cards is shuffled. Cards are dealt face up one at a time until an ace appears.

1) What is the probability that the first ace appears on the third card?
2) Show that the probability of getting the first ace on or before the ninth card is greater than 50%

Looks pretty straightforward. There are 52 cards and 4 of them are aces. The probability the first card is drawn is an ace is 4/52= 1/13. The probability the first card is not an ace is (52- 4)/52= 48/52= 12/13.

If the first card is NOT an ace there are still 4 aces but only 51 cards so the probability the second card is an ace is 4/51. The probability that the second card is not an ace is (51- 4)/51= 37/51.
The probability the first card is not an ace and the second card is an ace is (12/13)(4/51). The probability the first two cards are not aces is (12/13)(37/51).

If the first two card are not aces,, there are still 4 aces but only 50 cards so the probability the third card is an ace is .....

For some reason this stuff isn't making that much sense :/