The Postdoc Problem (Pick Second-Best)

Four applicants of distinct unknown qualities arrive in uniformly random order; after each you learn only its rank relative to those seen so far and must irrevocably accept or reject (if you reach the last you must take it). A famous twist: you win only if the applicant you accept is the SECOND-best of all four (the very best is taken by a rival institution, so picking the best is a loss). Find the optimal policy and the maximum probability of landing exactly the second-best.