This is only true if you have a pretrained base model trained on infinite true data with no bias. In practice it will have picked up some bias, maybe it encountered more famous "James" birthdays in January and on a digit starting with 2, so Jan 2 and Jan 20-29 has a higher probability than all. But finetuning and especially RL completely breaks these probabilities as a measure of certainty because the goals shift from generally modelling text to something else entirely.