probability vs. trials: a special case where the number of draws is not constant

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I have 3 cards of color heart one of them is Ace AND one other card of type spade to make all together 4 cards

the success is when I draw Ace heart

a player must draw the Ace heart within a number of trials.

it counts as a trial if a heart card is drawn otherwise, it does not count as a trial (if I draw the spade card)

I draw a card at one time. depending on the type of the card we increment the number of trials by 1 or by 0

now I know that the probability to draw the Ace heart is 1 if I am allowed to have maximum of three trials. however, I could not write this in a neat probabilistic way.

PS: my original problem is 67 cards one of them is my card of interest plus 13 cards that do not count as a trial if I pull them.

it would be more helpful form me if I could build a table for permitted trials vs probability regards