Independent impressions (= inside view in your terminology), though my all-things-considered belief (= betting odds in your terminology) is pretty similar.
Though I understood what you meant, perhaps a clearer terminology is all-things-considered beliefs vs. independent impressions.
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?