Aces Before Kings: Probability via Exchangeability

You shuffle a standard 52-card deck uniformly at random and reveal cards one by one without replacement. Let $T$ be the first time you have seen all four aces or all four kings (whichever group is completed first). Compute $P(\text{aces finish first})$ -- that is, the probability that all four aces appear before all four kings are complete -- and justify your answer rigorously using a symmetry or exchangeability argument. No lengthy enumeration.