No analogy needed. It's actually because "Yes it exists" is a linguistically valid sentence and each word is statistically likely to follow the former word.
LLMs produce linguistically valid texts, not factually correct texts. They are probability functions, not librarians.
Transitors at the quantum level are probability functions just like everything else is. And just like everything else, at the macro level the overall behavior follows a predictable known pattern.
LLMs have nondeterministic properties intrinsic to their macro behaviour. If you've ever tweaked the "temperature" of an LLM, that's what you are tweaking.
Temperature is a property of the sampler, which isn't strictly speaking part of the LLM, though they co-evolve.
LLMs are afaik usually evaluated nondeterministically because they're floating point and nobody wants to bother perfectly synchronizing the order of operations, but you can do that.
LLMs produce linguistically valid texts, not factually correct texts. They are probability functions, not librarians.