https://en.wikipedia.org/wiki/Monte_Carlo_method

If it's out of distribution, you're more likely to get a chaotic distribution around the answer to a question, whereas if it's just not known well, you'll get a normal distribution, with a flatter slope the less well modeled a concept is.

There are all sorts of techniques and methods you can use to get a probabilistically valid assessment of outputs from LLMs, they're just expensive and/or tedious.

Repeated sampling gives you the basis to make a Bayesian model of the output, and you can even work out rigorous numbers specific to the model and your prompt framework by sampling things you know the model has in distribution and comparing the curves against your test case, giving you a measure of relative certainty.

Sounds like just not using an LLM would be considerably less effort and fewer wasted resources.