P(X2=0)=7/12 is false
It doesn't matter when you select.
If you don't have any info on the first selection the probability is the same.
The probability that the first card from a deck is the ace of spades is 1/52.
The probability that the tenth card is the aces of spades is also 1/52.
If you give me some info on the first nine cards, then the probability changes.
So P(X_1=0, X_2=0)=P(X_2=0|X_1=0)P(X_1=0)= (7/12)(8/13)