Seeking mathematician for story's analysis

While I'm writing a story where a character tries to solve a problem using meta-uncertainty, I know a useful trick is to treat uncertainty on a logarithmic scale rather than a linear one, as that comes closer to usefully representing how increasing evidence increases certainty.

I'm working with a problem where the character's reasoning process itself is questionable, and so it's uncertain that the calculated most-accurate-possible level uncertainty is actually the most accurate possible level. I'm guessing that it may be useful to treat the calculated level of uncertainty as a normal Guassian distribution, with the X scale measured in logarithmic confidence units (" decibans ").

Converting the graph from a logarithmic scale to a linear one would seem to do interesting things. Using some rules of thumb and guesstimation, my current draft of the relevant paragraph reads:

"Let's see - let's say that my best guess, the centre of the curve on the logarithmic scale, is at ten decibans, with a standard deviation of something near ten decibans. About the only thing I remember about standard distributions is that a squidge over two-thirds of the area under the curve is within one standard deviation, and ninety-five percent within two. So something like, mm, a seventh of the probability mass would be between minus ten and zero decibans, a third from zero to ten, a third from ten to twenty, and a seventh from twenty to thirty. Converting from decibans to linear probability, a seventh of the probability would be between ten percent and fifty percent, a third from fifty to ninety percent, a third from ninety to ninety-nine percent, and a seventh from ninety-nine percent to ninety-nine point nine. Pretending for a minute that each of those four buckets have their probability equally spread out, and taking the averages, let's see... an average of somewhere around seventy-five percent.

If this character then consulted an actual mathematician, how much correction would be needed to turn this approach into a useful certainty estimate?

Thank you for your time.