Whoa!!! That is WAY too small. There are only ways to pick teams. You have selected one such way. There are only four ways to achieve the one way you have selected, that is, they must be selected together in one of the four selection rounds.

Pr(Selected in the first round) = (1/4)^4

The problem with the next step is that not all paths lead to the desired result. If any of the four teams is selected in the first round, they all must be. If any of the four teams is selected in the first round, but any of the others is not, the process ends. The ONLY way to get to round two is for NONE of the teams to be selected in round 1. There are only a few ways to do that.

Pr(None selected in round 1) = (3/4)^4

Thus, Pr(Selected in round 2) = (3/4)^4*(1/3)^4, since round 2 doesn't exist without its dependence on the outcome of round 1.

Using the same logic:

Pr(Selected in round 3) = (3/4)^4*(2/3)^4*(1/2)^4

If we get to round four with hope, obviosuly they will be selected together.

Pr(selected in round 4) = (3/4)^4*(2/3)^4*(1/2)^4*(1)^4

Thus, (3/4)^4 + (3/4)^4*(1/3)^4 + (3/4)^4*(2/3)^4*(1/2)^4 + (3/4)^4*(2/3)^4*(1/2)^4*(1)^4 = 4*(1/4)^4 = 0.015625