jmc

We have two cases because if the first card is a King, it could be a $♡$ or not be a $♡$.

There is a $\frac{1}{52}$ chance that the King of $♡$ is drawn first, and a $\frac{12}{51}=\frac{4}{17}$ chance that the second card drawn is one of the twelve remaining $♡$, which gives a probability of $\frac{1}{52}\times \frac{4}{17}=\frac{1}{221}$ chance that this occurs.

There is a $\frac{3}{52}$ chance that a non-$♡$ King is drawn first, and a $\frac{13}{51}$ chance that a $♡$ is drawn second, giving a $\frac{3}{52}\times \frac{13}{51}=\frac{1}{68}$ chance that this occurs.

So the probability that one of these two cases happens is $\frac{1}{221}+\frac{1}{68}=\boxed{\frac{1}{52}}$.