Wether they know or not doesn't really matter. They won't give us that information either way.

I would like to say that we can infer the probability distributions from players experience, just by plotting the number of times an upgrade/refinement has succeded at a certain value as a function of the total number of maximum chances before success.

However, i do not believe (from personal experience) that the probability distribution remains constant at all levels. For example, upgrading anything from lvl 1 or 2 to 2 or 3 usually requires less than 5 tries out of 20 or 30. In other words for the first 2 levels a 20% filled bar will usually result in a successful upgrade/refine. However once you reach lvl 4 or 5 you usually need 80% or more of the bar for a successful upgrade/refine.

Although this only takes into account my experience when lvling up charms/tactics/refinement/battle armor and is not a very big sample, this behavior uis surprisingly consistent. Thus i believe that the probability distribution for the low levels peaks earlier than the distribution for the latter ones. Also this is supported by the fact that i know no one who needed 18+ tries to upgrade from lvl 1 to 2 however i have seen players who needed 65+/70 tries to upgrade at lvl 4.

Also i have noticed that its rare for an upgade/refinment to succeed at the middle values, its usually successful whe the first or last quarter of the bar is full. So i do not believe that the probability can be linear.

Those are my observations, again my sample is only me and what i have seen on the forums from time to time. It only serves to give a tendency and not the full behavior.