Non non probability Haar measure on locally compact group

Question

Suppose that $G$ is a locally compact group, which is not compact. I know that in general there is no way to "normalize" the Haar measure on $G$. But can we say, in general, that the Haar measure is not a probability measure on $G$? Are there examples of non compact, locally compact groups with a Haar measure which is a probability measure? Thanks!

Answer 1

The Haar measure on a non-compact group is an infinite measure and thus not a probability measure.