Let $k$ denote the event that the card drawn is king.

We have to find $P(k/kkk)$

Now $P(k)=\large\frac{4}{52}$

$P(k/k)$ is the probability of a second king with the condition that one king has already been drawn.Now there are 3 kings in (52-1)=51cards

$\therefore P(k/k)=\large\frac{3}{51}$

$P(k/kk)$ is the probability of a third king with the condition that two kings have already been drawn.Now there are 2 kings in (52-2)=50cards

$\therefore P(k/kk)=\large\frac{2}{50}$

$P(k/kkk)$ is the probability that three kings have already been drawn.Now there are 2 kings in (52-3)=49cards

$\therefore P(k/kkk)=\large\frac{1}{49}$

Step 2:

By multiplication law of probability we have $P\big(\large\frac{k}{kkk}\big)$$=P(k)\times P(\large\frac{k}{k})$$\times P(\large\frac{k}{kk})$$\times(\large\frac{k}{kkk})$

$\Rightarrow \large\frac{4}{52}\times\frac{3}{51}\times \frac{2}{50}\times \frac{1}{49}$

$\Rightarrow \large\frac{24}{650740}$

$\Rightarrow \large\frac{1}{270725}$