I have now also added a visual display of those probabilities over time (I called this the Bird's Eye view last season). You can find the graphs here. Each team is represented by a color on the graph (I tried to use official team colors). The legend on the right is in the same order of the stacking, and you can also just mouseover the graph for the detail. Here is a smaller version of the graph for reference:
The point of the graph is to show how each team's share of the Finals win probability shifts from day to day. Since there can only be one champion, Finals win probability is a zero-sum game (or one-sum, I suppose). Any gains in one team's win probability has to be withdrawn from the accounts of the other teams. What is interesting is that when a team loses a game and its win probability drops, the benefit doesn't always accrue to the team that beat them.
For example, take the Bulls Game 1 victory over the Heat on May 6. Going into the game, the Heat had a win probability of 51%, and after the loss, it dropped to 40%. But the Bulls only saw their Finals win probability increase from 0.02% to 0.5% (they are barely visible on the graph). The big winners were the Spurs and the Thunder, with the Spurs seeing a 5% rise in Finals win probability and the Thunder seeing a 3% rise. Basically, the Bulls victory increased the likelihood that the Spurs or Thunder wouldn't even have to face the Heat in the Finals (should they make it that far).
There is a dropdown at the top of the graph that allows you to view the win probabilities of any round of the playoffs. I ordered the teams so that the probabilities "stack" nicely.
Comparison to Vegas
As of today (May 11), my simulations have the Heat as the favorite (of course) with a win probability of 62.5%, which appears to be where Vegas has them as well. After that, my probabilities seem to diverge a bit from the sportsbooks.
I think San Antonio may be overvalued in my rankings right now (and thus have an overvalued Finals probability), due to their "endgame" with the Lakers in round 1. The Spurs GPF (Generic Points Favored) jumped up in Game 3 and Game 4 of that series, but I think that was more a function of the Lakers' injury troubles (and the fact that they had probably given up at that point). While I think the responsiveness of my rankings is a nice feature in the regular season, it can be a bit of a "bug" during the playoffs. When the point spread started tilting more and more in favor of the Spurs, my model had no way of knowing whether that is due to the Spurs getting better or the Lakers getting worse. Without other games to break the tie, it effectively just splits the difference between the two teams. The Spurs' ranking has come back down to earth a bit in Round 2, but I think there may still be some residual effects.