Proof of a key agreement protocol based on bilinear pairings
however... I can't see how they deduce $Pr[A_k] ≥ η(k)$ from the last expression.


They use the upper bound $Pr[E\text{ succeeds}|A_k]Pr[A_k]\leq Pr[A_k]$, which follows from the fact that $Pr[E\text{ succeeds}|A_k]\leq 1$.