Instead of calculating:
\begin{equation} \left( \frac{52! -1}{52!} \right) \end{equation}
We calculate the log of it because then you are able to write:
\begin{equation} \log \left( \frac{52! -1}{52!} \right) = \log (52! - 1) - \log(52!) \end{equation}
which won’t be rounded to 0.