Nat claimed her stuff is random, so why think that?
Well, on day 2, when Luthon was explaining his ability, I recall Juliet saying that his ability works similar to hers. So I assumed that she knows the ability that her target uses that night.
Also, Kvothe quoted Juliet's post where Juliet said that Observational haki was one of Kvothe's abilities and said she did not like Midnight's vote on Tris.
So putting these 2 together, I assumed that Kvothe used observational Haki on midnight last night.
@Kvothe Kingkiller this is why I thought you targeted Midnight ^