Claims arrive in an insurance portfolio, according to a homogenous Poisson process $X(t), t\geq 0$. Assume that each of the $12$ months in a year has exactly $30$ days. Calculate the value of the following conditional probability:
\begin{equation*} P\{X(2) = 3, X(3) = 5 | X(4) = 5\} \end{equation*}
where $X(k)$ is the number of claims during the first $k$ months of the year. Can anyone help?