Check if $a<b$ in a trustless scenario
This is a common misunderstanding of zero knowledge. In order to prove something in zero knowledge (in fact, in order to prove anything in a way that is non-trivial), there must a well defined statement. See https://crypto.stackexchange.com/a/60633/25354 for an explanation of this.

Note that in your context, it is always true that there exists some $b$ such that $a&lt;b$ (over the integers). Thus, without having some commitment or encryption of $b$ before the proof starts, this is trivially always true.