Think of it like this.
What is the probability that first card is an ace
What is the probability that second card is also an ace (given that the first card already drawn was an ace)
Hence the probability that I get a pair of aces when I draw two cards
= 4/52 * 3/51
Now we have 13 card numbers eg: Aces, Kings, Queens, Jacks ....
Therefore there are 13 ways in which I can perform step 1 and step 2 , asking questions like What is the probability I get a pair of kings when I draw two cards....
and the answer for each of these 13 steps = 4/52 * 3/51
Therefore total probability of having any pair when we draw two cards
= 13 * 4/52 * 3/51
thanks for such clear explanation!