Independent impressions (= inside view in your terminology), though my all-things-considered belief (= betting odds in your terminology) is pretty similar.
Depends on who asks, why, and how much context we share. Much of the time, I give the "signaling answer", which is neither my inside/true estimate nor a wager I can make.
It's not purely signaling - I'm not JUST trying to convince them I'm smart or to donate to my preferred cause or change their behavior or whatnot. It also includes a desire to have interesting conversations and to elicit models and predictions from my discussion partners. But it's not a pure estimate of probability.
I give it somewhere around p(personal death) = 0.999, p(most humans die with me) = 0.15, and p(humans wiped out within a few hundred years) = 0.8.
There has been some confusion about whether people are using inside views or all-things-considered betting odds when they talk about P(doom). Which do you give by default? What are your numbers for each?