Community wiki answer so the question can be marked as answered:

As noted in the comments, your calculation is correct but somewhat unnecessarily complicated. You don’t need to consider the order of the remaining $51$ cards; that just multiplies both the numerator and the denominator by $51!$ and cancels out. There are $4$ kings and $13$ hearts, which would be $4+13=17$ cards, but one card is both a king and a heart and needs to be subtracted back out, so there are $16$ you’re looking for out of a total of $52$, for a probability of $\frac{16}{52}=\frac4{13}$.