Most probability problems are easier to solve when solving for the chance something *won't* happen, for some reason, although trying to do that with 5 appears to give me -8%, so I'm going to do the longer route.

We can start by first listing all ways that Beta can win. Namely, B-B-A, B-B-B, B-A-B, and A-B-B. BAB and ABB are technically the same thing because the order doesn't affect the outcome, so I will solve them once and double the chance. Similarly, the final game has no effect on the outcome if Beta wins the first 2 games, so we can simplify BBA + BBB to BB_ (the blank is there to represent the unplayed final game).

BB: The chance of Beta winning the first 2 games is equal to their chance of winning one game squared (chance of B winning * chance of B winning = chance of B winning in any 2 given times, a.k.a. the first 2 times now.) 40% * 40% = 16%, so BB = 16%.

ABB and BAB: We can assume Alpha won the first game, as the order doesn't matter (it's just who won more games, not who won which game when). Therefore, ABB = 60% * 40% * 40% = 9.6%.

Now that we have all of the outcomes covered, we can add them. BB + BAB + ABB = 16% + 9.6% + 9.6% = __35.2% chance that team Beta wins the championship.__

Hope this helped!