Less probable also means less optimal and you get a subpar response. More so if it's baked into its reasoning. It's intelligence will suffer unless this is some post processing thing.
You can hide data in that randomness without impacting the quality of the response by using a sufficiently "random looking" pseudorandom bit stream instead of real random numbers.
I previously worked on a project to do that here: https://github.com/shawnz/textcoder
A small anecdotal example to demonstrate how the response lacks depth. It's imperceptible to most. You'll probably see through it in your own field of expertise, if you had both answers. Uncanny valley type thing.