HOW a presidential candidate conducts himself in his private life does relate to his success or failure. Nelson Rockefeller's divorce wrecked his presidential prospects. Gary Hart's frolicking put an end to his quest for the White House. And Chappaquiddick has kept Ted Kennedy from capturing the Democratic nomination.It was doubtless with this in mind that Arkansas Gov. Bill Clinton came to a Monitor breakfast the other morning armed with a statement about his private life that was intended to clear the air. The question and answer session had gone on for about 20 minutes when a reporter asked the "Have you ever?" question about extramarital affairs. Governor Clinton laughed and quipped: "I thought you would never ask." He said the question stemmed from "all those rumors about me during my race for governor that were sparked by a disgruntled state employee who was working for my opponent. Those were false and I said so at the time." Here Clinton spoke of his relationship with his wife, who was at his side. "What you need to know about Hilary and me is that we've been together nearly 20 years. It has not been perfect or free from problems, but we're committed to our marriage and its obligations - to our child and to each other. We love each other very much." At the outset of the breakfast the governor was asked the question that had drawn nearly 50 journalists to this gathering: "Are you going to run?" His reply: m obviously pretty close or I wouldn't be here bothering you this morning." It was obvious, too, that he was also on hand to put an end to rumors that he and his advisors believed might cloud a presidential candidacy. Perhaps he succeeded. Several reporters I talked to afterward said they thought Clinton was wise to address this potential problem early, and that they felt his answer was persuasive. One veteran newsman saw it differently, however. "I believe Clinton," he said. "But if he becomes the presidential nominee you can be sure that someone or some group will use these rumors against him. You'll get an ad like the Willy Horton ad that contains false innuendoes. That's the way it goes in a presidential campaign." Sadly, this could be true. I'm reminded of the charges against President Ford during his race with Jimmy Carter in 1976. Ford was accused of unethical conduct regarding some trips he had taken. Only after the election was over - and after some voters may have voted against him because of this allegation - was Ford cleared of suspicion. Another reporter had this view of Clinton: "I really don't care what he does in his private life, short of committing some crime, of course. The only thing that's important to me is how good a governor he is - or how good a president he would become." In a more permissive America this newsman's view could reflect the attitude of a growing number of voters. But it certainly isn't a prevailing view. Presidential candidates know that most Americans still apply what are called "family values" to those who seek the White House. Clinton knows about these voter expectations. That's why he was responding to them. Most Americans have only one impression of Clinton: When he talked on endlessly while delivering a nominating speech at the last Democratic convention. He somehow misread his audience that night. "I talked for several months," he said, now able to laugh about it. He obviously learned his lesson. Clinton, a former Rhodes Scholar, is graded by his fellow governors as one of their best. And he is positioned to use the successful Jimmy Carter approach to winning the presidency: He's a southerner, an outsider, and he has an agenda that will mark him as an independent thinker set on solving problems rather than pursuing the social changes demanded by the liberals.