I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a proportion. I could use easily a normal distribution with really small variance but our professor said that it would be incorrect because the support is the whole $\mathbb{R}$ and $\theta\in [0,1]$.Thus, I restricted my self to beta distributions but I cannot find a point mass beta distribution.
So I would like some help in order to find such distribution even if it's not a beta distribution.