Gaussian prior favors values closest to zero?

Question

I am reading an article on Bayesian Logistic Regression, where they're using Logistic Regression, imposing a Gaussian prior (with mean = 0) on its parameters. They state that a Gaussian prior favors the values of the parameters to be near zero, but not exactly zero.

My question: if the mean is zero, how could it favor the parameters not being exactly zero?

The article I'm referring to is this (Section 3).

Thanks.

Answer 1

It appears to me that what is meant is simply that although the probability that the parameter is near $0$ is high, the probability that it is exactly $0$ is $0$.