Pounding the Beltway in his big black Lincoln, Maryland state Sen. Edward T. Conroy heard the devasting news on his car radio, as an announcer declared one of his opponents the winner in the race Tuesday night for the Democratic U.S. Senate nomination.

Within the hour, a dazed and dishearted Conroy walked into his election night party at the Baltimore hotel and went straight for his campaign chief.

"What am I behind?" he asked Dennis Devaney, who by then was clutching the candidate's shoulders.

"You're not behind at all," came the swift reply.

In the next two hours, Conroy pulled steadily away from his 11 opponents and ended the night defeating the closest rival by better than 26,000 votes.

Yesterday, Conroy found himself behind again -- facing the popular two-term Republican incumbent Sen. Charles McC. Mathias, already the heavy favorite in the general election race.

As Conroy savored his primary victory at his Bowie home, he said, "I'd rather go in as the underdog . . . I like underdogs."

No one came forward to argue with that assessment by Conroy of his chances in November.

Several prominent Democrats said privately that Conroy has little hope of knocking off Mathias, despite a three-to-one registration advantage by Democrats over Republicans in the state.

And State Democratic Chairman Rosalie S. Abrams, who serves in the state Senate with Conroy, hedged her support of his candidacy.

Asked if she would "support Conroy's candidacy enthusiastically," Abrams pointedly answered, "I will support his candidacy, as the state party chairman."

Then Abrams added: "Ed Conroy will work hard to pull off a victory, and will give Mathias a good battle."

The question of how the contest will be fought was unclear yesterday.

Rep. Gladys Noon Spellman, like Conroy a Prince George's County Democrat, guessed that challenger Conroy "will define the issues" against the incumbent, but Spellman conceded that she doesn't know "what Ed intends to bring up."

Conroy wasn't prepared to enlighten her or the voters yet.

"I would prefer not to talk about the issues at this time," he said, leaning back behind a colonial desk in his at-home office. "We're going to have a think-tank approach . . . my people will come out with white papers, and then I'll talk about them."

Mathias, who easily won renomination in a five-way Republican primary said that he is "very interested in knowing what his [Conroy's] particular interests and causes are."

Asked if it might turn out that Democrat nominee Conroy is more conservative than the Republican incumbent. Mathias said "it's a very complex time" and such labels are not easy to assign. "On some matters, I may be more conservative than he is, but I don't know enough about where Ed has been to say."

As to the effect of a Reagan candidacy on his own chances, Mathias said: "I have said all along that I could support any of the Republicans running."

Conroy, calling Mathias "a minority within a minority, a Republican out of step with his own party," promised to give his rival "a fight better than he's ever had before."

In sailing to a second term six years ago, Mathias carried all 23 counties, losing to Democrat Rep. Barbara A. Mikulski only in her native Baltimore City. Mathias piled up a huge advantage in the Washington suburbs, getting a 65,000 vote advantage in Montgomery County alone.

But Conroy figures to do better than Mikulski did in Prince George's County, which Mathias carried in 1974 by 18,000 votes.

Indeed, it was Conroy's own Prince George's County that carried him to the nomination on Tuesday. All but 3,000 votes of his victory margin came in Prince George's. Conroy also predicted that he would "run well in Baltimore City and the rural areas," and would work hard for support in voter-rich Baltimore County.

The 51-year-old lawyer conceded that money will be a major problem in the race. "I'll run a respectable campaign as far as dollars are concerned, but no way will I raise more money than Mac," Conroy said.

Conroy spent less than $50,000 in the primary, $22,000 of it from his own pocket, while Mathias spent about $175,000 -- more than the entire gang of 12 Democratic aspirants combined -- and still had money left over to begin the general election campaign.

Conroy spent yesterday taking calls from well-wishers, planning a short vacation to Ocean City and working on healing wounds within the party caused by the wide-open primary. Said the senator: "The healing process will be quick."

Mathias wasted little time celebrating his victory. The senator showed up at a senior citizens meeting in a Baltimore union hall at 9 a.m., and planned to finish a busy day of campaigning last night by speaking to the Maryland Hospital Association at the Hunt Valley Inn.