Answer
${\bf 4.0}\;\rm m^{-1}$
Work Step by Step
We know that the probability density is given by
$$\text{Prob}( \text{in } \delta x \text{ at } x)=P(x)\delta x=\dfrac{N }{N_{tot}}$$
where $N_{tot}$ is the total number of photons, and $N$ is the number of photons detected at position $\delta x$.
Hence, the probability density is then
$$P(x) =\dfrac{N}{N_{tot}\delta x}$$
Plug the known;
$$P(x) =\dfrac{(2\times 10^9)}{(5\times 10^{12})(0.1\times 10^{-3})}$$
$$P(x) =\color{red}{\bf 4.0}\;\rm m^{-1}$$
