astrophysics - Relationships between optical depth, $tau$, and probability of being scattered

The optical depth is given by many as:

$$\tau=n_e\sigma_{cs}L$$ Where $n_e$ is the number density of the medium, $\sigma_{cs}$ is the scattering cross section and L is the linear extent of the medium.

I was wondering, what is the relationship between the optial depth and the probability of scattering? I can't seem to find it amongst online lecture notes and other sources. A really concise answer would be appeciated.