Let us start from the event space $\Omega$. Pretend that there exists $\Omega_p$ such that $\mathbb{P}(\Omega_p)=1$. I know that
the events set difference $$A\backslash B\tag{1}$$ is a subset of the complement of $\Omega_p$, i.e. a subset of $\Omega_p^C$.
Since we know that $\mathbb{P}(\Omega_p)=1$, it follows that $\mathbb{P}(\Omega_p^C)=0$, that is $$\text{"almost no point is in } \Omega_p^C\text{"}$$
Hence, what does it mean that $$A\backslash B\subset\Omega_p^C\tag{2}$$ ?