There are 52 possible outcomes when you draw one card from a standard deck. Hence, 52 is the denominator of your probability fraction.
There are two ways to look at calculating the numerator. You can say that there are 13 diamonds plus 3 kings that are not diamonds for a total of 16, or you can say that there are 12 diamonds that are not a king plus 4 kings, again for a total of 16.
So, 16 over 52. You just need to reduce the fraction.
My calculator said it, I believe it, that settles it