What is the probability of choosing a king on the second draw if the first was a king without replacement?

There are 4 Kings in a standard pack of 52 cards.

If 1 King has previously been drawn this now leaves 3 kings out of a total of 51 remaining cards. The probability of now drawing a King is therefore 3/51 which simplifies to 1/17.

Note: this is the probability concerning the 2nd draw only.