When Sen. Olympia Snowe made her sudden decision not to run for a fourth term, it gave Democrats their best chance in years to reclaim a Senate seat they held for most of the last two generations. Now, it probably won’t happen, and therein lies an instructive political tale.

Snowe withdrew on Tuesday, Feb. 28, just two weeks before party filing deadlines. That Friday, 2nd District Rep. Mike Michaud took himself out of contention, leaving one prominent office-holding Democrat – 1st District Rep. Chellie Pingree. National groups announced support, expectations rose, but Pingree hesitated, calling it “a difficult decision.”

Furious political discussion ensued that weekend and, on Monday, the unexpected happened. Former Gov. Angus King announced he was in, as an independent, and started showing off his political skills. He endorsed President Obama but said he wouldn’t decide whether to caucus with Republicans or Democrats in Washington. Both decisions play well with potential constituents.

King had no reason to rush. His filing deadline wasn’t until June. But he seized the initiative, and by Thursday Pingree was out. What happened?

An old political story is suggestive. In 1937, Lyndon Johnson, just 28, had served as a congressional aide and was administrator of a New Deal jobs program (back then, the government actually had them.) His Texas district’s congressman, chairman of the powerful Appropriations Committee, died suddenly. Everyone expected his 62-year-old widow to run, and she called a press conference for Monday.

Johnson was ambitious, but he, like every other aspirant, hung back. That weekend, Johnson visited his father, Sam, who told him, according to biographer Robert Caro, that “You haven’t learned anything about politics.” Sam urged Lyndon to announce immediately. The widow didn’t really want to run, he said. Faced with a fight, she’d withdraw.

Johnson called reporters, and got the story in the Sunday papers, saying he was in the race to stay. On Monday, the widow dropped out. Although Johnson faced several better-known rivals, he’d gotten the jump on them, and won the seat easily. Poor hill country farmers voted for him and he never forgot, launching the War on Poverty when he became president 26 years later.

Pingree and King have a close relationship. She was the Legislature’s Senate majority leader when he was governor, and Democrats were trying to avoid the rancor that marked the single term of Gov. James Longley, the only previous independent governor.

Democrats and King got along, even though King, too, entered office vowing to cut the state work force and advocating welfare reform. King became a mentor for Pingree. So when Snowe withdrew, the same facts arguing against a King candidacy – at 68, he’s 11 years older, and was out of politics a decade – actually gave him an advantage.

Once King announced, Pingree wasn’t going to run. By that time, calculation had replaced ambition. In her one candid statement, she told a Portsmouth Herald reporter, “We have seen three-way contests before become very complex, and I didn’t want to take the chance that my entering the race would make it more likely for a Republican to be the next senator.”

Former Gov. John Baldacci, Democrats’ last big name, never appeared serious, even though he waited until the end to opt out.

Now, it’s hard to see anyone other than King getting elected. There will be competitive primaries, and some Rs and Ds are interesting possibilities.

For the Republicans, Rick Bennett, former Senate president, has an independent streak – he supports environmental programs and Clean Elections – and should be well-funded. For Democrats, former Secretary of State and House member Matt Dunlap – who joined the race with Snowe still in – appeals to different party factions and could be an effective debater. But for any R or D to gain traction, King would have to stumble.

Even the most successful politicians will tell you that winning often depends on luck, and timing. Candidates can’t do much about luck, but they can control timing. Angus King did exactly that, and as a result could be on his way to the Senate.

There could be another explanation for Pingree’s curious hesitation – that she wants to run for governor in 2014. That’s where she was headed in 2002 when she was derailed by Baldacci, who convinced her to make a U.S. Senate bid against Susan Collins.

John McKernan, Joe Brennan, and Baldacci have all left Washington to run for governor, two successfully. We won’t know whether Pingree plans to join them for another year or so.