This is a general question but to make it simpler I have defined an example and hope someone could come up with a more general answer if this is actually defined.
Given a multivariate normal distribution (in 2D with x and y for this example) one can define the conditional distribution of $p(y|x)$ (https://statproofbook.github.io/P/mvn-cond.html)
However, if one is given an interval over x (ex. x \in [x_1, x_2] ), is it possible to define the conditional distribution of y : $p(y | x_1 < x < x_2)$?
Similarly, if one is given a univariate normal over x (ex. $x \sim \mathcal{N}(\mu*, \sigma*)$, is it possible to define the conditional distribution of y : $p(y | x \sim \mathcal{N}(\mu*, \sigma*))$?