= Solution
The conditional <probability> of the atomic ground state is the squared ground-state <amplitude> divided by the five-photon event <probability>:
$$
\boxed{P(g\mid5)=\frac{|c_4|^2\sin^2(g\sqrt5\,t)}{|c_5|^2\cos^2(g\sqrt6\,t)+|c_4|^2\sin^2(g\sqrt5\,t)}.}
$$
For $z\ne0$, $|c_5|^2=|z|^2|c_4|^2/5$, giving the equivalent expression
$$
\boxed{P(g\mid5)=\frac{5\sin^2(g\sqrt5\,t)}{|z|^2\cos^2(g\sqrt6\,t)+5\sin^2(g\sqrt5\,t)}.}
$$
It applies only when the conditioning denominator is nonzero. The distinct $\sqrt5$ and $\sqrt6$ factors reflect the two different initial photon-number blocks.
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