If $P(T\mid X) = a$ and $P(T\mid Y) = b$, what is $P(T \mid X\cap Y)$?

Question

Is it possible to figure out $P(T\mid X\cap Y)$ if we know $P(T\mid X)$ and $P(T\mid Y)$?

Extra Information: $X$ and $Y$ are non-mutually exclusive while $Z$'s relationship with $X$ and $Y$ is arbitrary. The probability distributions are also arbitrary.