Naming a restricted probability space

Question

Consider a probability space $(\Omega,F,P)$.

I want to consider $(\Omega',F',P')$, where $\Omega'\subset\Omega$ is nonempty event such that $P(\Omega')>0$, and $F'=\{\omega\cap\Omega'\mid\omega\in F\}$, and $P'(\omega')=P(\omega\cap\Omega')/P(\Omega')$.

Then, this would be a probability space and I believe there should be a name to call this.

Question: How do we call this space?