Probability distribution of a Gaussian knowing that a variable is in a certain interval.

Question

Suppose that we have a variable $X$ with a normal distribution with mean 0 and variance $\sigma$. We also have a machine that tells us with 100% fiability if $|X|>\sigma$ or $|X|<\sigma$, I would like to know the probability density function of $X$ given that the machine told me that $|X|>\sigma$ (also the other probability density function, with $|X|<\sigma$). I thought about just renormalizing the gaussian in the given intervals (I believe this would lead me to a wrong answer) or using Bayes' Theorem, but I don't know how, could anyone give me hints/help? Thanks