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Prime Minister Stephen Harper’s path to a fourth term is narrowing in Canada, with polls suggesting there’s little chance he’ll win another majority government and his two top rivals ruling out supporting a Conservative minority.

Harper, who took power in 2006, governed with a minority during his first five years in office. Polls show his Conservatives locked in a narrow three-way contest with the Liberals and the New Democratic Party ahead of the Oct. 19 vote, with no party currently projected to win a majority of seats.

“The short answer to your question is, there isn’t a snowball’s chance in hell,” NDP Leader Tom Mulcair said Wednesday in Montreal when asked whether he’d support Harper in a minority.

Liberal Leader Justin Trudeau was equally categorical. “There are no circumstances in which I would support Stephen Harper to continue being prime minister of this country,” he told reporters Tuesday, also in Montreal.

Both opposition leaders ruling out support suggests that even if the Conservatives win the most seats in a minority situation, Harper won’t be able to command enough support in the House of Commons to remain prime minister.

Neck and Neck

National averages compiled by polling aggregator ThreeHundredEight.com show the Liberals with a statistically insignificant edge at 30.5 percent, compared to 30.3 percent for the Conservatives and 29.7 percent for the NDP.

As the incumbent prime minister, Harper has the right to test the confidence of the House of Commons regardless of how many seats he wins. He would remain prime minister until he recalls parliament, and could wait weeks or months to do so.

If the Conservative leader fails to gain the confidence of the House, Governor General David Johnston -- Queen Elizabeth II’s representative in Canada who was appointed by Harper -- would likely offer another party a chance at governing before calling another election.

Canadian elections in 2004, 2006 and 2008 produced minorities, before Harper won a majority in 2011. There are 338 seats in the legislature, meaning a party must win at least 170 to secure a majority.