My understanding was that ChatGPT simply puts a probability distribution over the next word, so I don't see why it's not as simple as just reporting how high those probabilities were for the answer it gave, relative to whatever would be typical.
Those values are probably not intelligible as confidence scores. For example if it answers a question with "They died in 1902", since there are a lot of euphamisms and rephrasings of 'died' it will get a relatively low probability. 1902 probably gets a high score, but you can't really rely on that since it might just as well be hallucinating and pulled the year from some famous event in that person's life.
