I want to represent a situation where a Bayesian agent believes that a certain quantity is uniformly distributed over an interval $[\underline{X},\overline{X}]$ but is uncertain on the value of $\underline{X}$ and $\overline{X}$. In other words, $\underline{X},\overline{X}$ are random variables and she might receive informative signals about them. In this sense, the agents' uncertainty is double layered, pertaining not only the value of the quantity, but also the distribution it follows.
My problem is how to represent such a situation, in the sense that I consider adopting a Bayesian Hierarchical Model where $\underline{X}\sim\mathcal{N}(\underline{x},1)$, $\overline{X}\sim\mathcal{N}(\overline{x},1)$, but I don't know how to introduce dependency between $\underline{X}$ and $\overline{X}$ so that $$\mathbb{P}(\underline{X}<\overline{X})=1$$ which is the condition ensuring that $\underline{X}$ and $\overline{X}$ almost surely define an interval.
I thought that random set theory (https://link.springer.com/book/10.1007/1-84628-150-4) might help here, but, in that field I am even less experienced than in Bayesian statistics.
Any help or reference would be much appreciated.