By Melissa Fares

NEW YORK (Reuters) - Democratic presidential nominee Hillary Clinton's probability of winning the White House got a modest bump in online betting markets on Tuesday, a day after her debate with Republican Donald Trump.

The price for a contract favoring Clinton on the popular PredictIt betting market was up 2 cents from Monday's post-debate closing and implied a 68 percent probability that she would win the Nov. 8 election.

Although during the debate Clinton was as high as 70 percent, her Monday night closing of 66 matched the highest closing number since her health took a stumble on Sept. 11. A pro-Trump contract on Tuesday indicated his probability for victory was 34 percent.

Trading in both contracts remained brisk on the heels of the first of three debates. PredictIt contracts are priced from 0 to 100 cents, with the contract price equating to a probability a candidate will win the election.

Initially, the price swings for both candidates were the largest since early August, though a substantial portion of Clinton's gain and Trump's fall had been retraced by early afternoon on Tuesday.

The swing following the debate put the brakes on a big Trump price rally on PredictIt that coincided with a tightening in most public opinion polls. On PredictIt, the implied probability of him winning had risen to 38 percent heading into the debate from 28 percent at the end of August.

Clinton's prospects also showed comparable improvement on betting sites based in Ireland and the United Kingdom. UK-based Betfair called the debate for Clinton based on odds movements on its platform, where more than 3 million pounds were bet during the event.

The implied probability of a Clinton win in November climbed to 69 percent on Betfair, the strongest it has been since her prospects took a hit over her pneumonia diagnosis this month. Trump's probability fell to 30 percent from 37 percent.

On Ireland's PaddyPower, Clinton's odds also had shortened, or improved, to 2-to-5 from 1-to-2 in the early moments of Monday's debate. Trump's odds, which initially lengthened following the debate, had shortened modestly to 2-to-1.

(Reporting by Melissa Fares and Angela Moon; Writing by Dan Burns; Editing by Howard Goller)