Princeton's email mentioned that they invited 100 candidates for interview, so if we take something like 25-35 as in previous years' number of admitted students, that'd be around 25-35% rate of admission among the interviewees.
I don't recall ever seeing the number of interviewed applicants from other programs like Columbia,
CMU, Berkeley etc. Considering how little we know I think it's better to not worry about it (not like you can do anything after taking the interview anyway) and focus your attention elsewhere. I have to admit I'm still tempted to check Quantnet forums to see if others heard back from any of those programs I've applied to though.