Property of equivalent measures

Question

Say I have a probability space ($\Omega, \mathcal{F}$) with two equivalent measures $\mathbb{P}$ and $\mathbb{Q}$.
Consider two sets $A, B \in \Omega$. I know that $\mathbb{P}\left[A\right] = \mathbb{P}\left[B\right] = k \in \mathbb{R}$ and $\mathbb{Q}\left[A\right] = z \in \mathbb{R}$.
Is there something (if it can be true) that allows me to say $\mathbb{Q}\left[B\right] = z$? Is it trivial from the definition of equivalent measures?