If the immediate next token probabilities are flat, that would mean the LLM is not able to predict the next token with any certainty. This might happen if an LLM is thrown off by out of distribution data, though I haven't personally seen it happen with modern models, so it was mostly a sanity check. But examples from the past that would cause this have been simple things like not normalizing token boundaries in your input, trailing whitespace, etc. And sometimes using very rare tokens AKA "glitch tokens" (https://en.wikipedia.org/wiki/Glitch_token).