Probability of a certain event is given as $f\left(\vec{x}\right)x^2$. This can be approximated to a delta function as follows \begin{equation} f\left(\vec{x}\right)x^2=k\delta^3(\vec{x}) \end{equation}
Here $f$ is a function of $\vec{x}$ and $k$ is a constant. I need to evaluate the value of $k$.
\begin{equation} k=\int f\left(\vec{x}\right)x^2d^3{\vec{x}} \end{equation}
What forms can $f$ have so that the value of k does not blow up when I integrate over the whole space.
Also, can a delta function be used as probability? shouldn't probability be finite?