What are the odds?

What were the odds that these two Major League Baseball teams, separated by only thirty-five miles of Baltimore-Washington Parkway traffic, would both be playing in the 2014 baseball playoffs?

The Baltimore Orioles, at home last evening, defeated the Toronto Blue Jays 8-2, to clinch the American League East title, and guarantee a playoff berth. The Washington Nationals, playing in Atlanta, defeated the Braves, their nemesis for much of the season, 3-0, securing the National League East title and a playoff spot.

What are the odds that —these American League Baltimore Orioles, in that Maryland city since 1954, and these National League Washington Nationals, who in 2005, brought baseball back to the Nation's Capital after a thirty-three year drought— that these two neighboring teams might play each other in the World Series, the Orioles not being there since 1983, the Nationals never? ^*

Whisper it; don't jinx it. The Cardinals, Dodgers, Giants, and Pirates, and the Tigers, Royals, Angels, and A's, all are yet barring the way. But dare to dream it.

In the National's locker room celebration last night, amidst the spraying of the Dom Perignon and the foaming of the Miller Lites, outfielder Jayson Werth drank a Bard's Beer, gluten-free. Two weeks from now, it's baseball in October: that magical, wonderful time. Anything could happen, and the beer —sorghum or barley-malt— will be cold.

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• ^* From Neil Greenberg at the Washington Post Fancy Stats:
  

  According to Fangraphs, the Nats have a 35.1 percent chance at making the World Series, while the Orioles sport a 18.8 percent chance. That means there is a 6.6 percent chance at these two meeting for all the marbles, or 14-to-1 odds.

  Thanks to reader Gregg Wiggins for pointing this out. See comments below.
• UPDATE 7 October 2014: The odds are zero. The Nationals were eliminated from the postseason by the San Francisco Giants, losing three games to one. The Orioles, however, continue on.