The withdrawal of Texas lawyer James A. Baker III as a candidate for the Republican national chairmanship has advanced the prospects of former Tennessee Sen. Bill Brock and politically embarrassed President Ford in his final days in office.

Baker, Ford's campaign chairman in the 1976 general election, dropped out of the race Monday to avoid being involved in a "a knock-down, drag-out fight."

But it became apparent yesterday that the fight is even more likely to take place with Baker out of the contest, although the chances of Brock's winning it have been greatly improved.

Baker's abrupt withdrawal left the President, the presumed titular leader of his part, without a candidate. Only last Friday, in an interview with The Washington Post, Ford had said he was prepared to risk his standing on Baker because there also was a risk in staying out of a contest so important to the Republican Party.

The decision of Baker to quit, partly because of a desire of his wife to avoid any acrimonious battles, was dismaying to the White House.

"Baker could have had the votes, but he didn't have the stomach for the fight," one Ford aide said.

At the time he withdrew, the count of Baker's supporters on the committee gave him 65 of the 162 votes, with 82 needed for election. Supporters of other candidates claimed this figure was high, but conceded that Baker might have the chairmanship because of White House pressure.

The absence of this pressure was a boon to Brock, who was defeated for re-election last November after one term in the U.S. Senate.

"I hope I might be able to pick up the votes of some of those who supported his (Baker)" Brock said in Nashville. "I am going to call those people who have indicated they would support him and see what we can do."

The President, meanwhile, was in no mood to attempt any new tries at king-making.

"I don't think he wants to get involved in the contest now," said deputy White House press secretary John Carlson. "He plans to sit it out."

Baker's withdrawal encouraged two state GOP chairmen to jump into the race. They are Kent B. McGough, 59, of Ohio, and Frederick K. Biebel, 50, of Connecticut.

Biebel's candidacy represented a holding action by the Northeast Republican chairmen, many of whom are miffed at the White House over the mismanagement of the Baker candidacy. McGough was regarded as a serious candidate, partly because he has the tacit backing of two influential Midwesterners - Wisconsin national committeeman Odij J. Fish and former national and Ohio chairman Ray C. Bliss.

While McGough is well-liked on the national committee, he has the draw-back of coming off a losing performance in Ohio. The GOP lost an incumbent U.S. senator in Ohio and the normally Republican state was carried by Jimmy Carter.

The Republican National Committee will choose the chairmen in open session Friday at the Washington Hilton. The other avowed candidates include:

Richard Richards, 43, the Utah GOP chairman and the front-runner with anywhere from 40 to 51 votes. He was the first candidate in the race and has the backing of Ronald Reagan, whom he supported in 1976. But the Reagan backing is a liability as well as an asset, since some members of the committee don't want any candidate who will perpetuate the Ford-Reagan division.

Brock, 45, who was touted last November by former National Committee Chairman Bob Dole as "a great organize." This is a widely held view and Brock's greatest asset. His liability is that some committee members doubt whether choosing a defeated one-term senator is the way to launch a national comeback.

Robert S. Carter, 52, the District of Columbia national committeeman and co-chairman of the party.He is popular with committee members and the apparent second choice of many of them. Carte ris the likeliest compromise if Brock and Richards dead-lock.

Thomas S. Milligan, 41, the Indiana state chairman. He is considered a competent chairman in a state where the party is highly professional. But Milligan is regarded as having been too pushy about his own prospective candidacy before Mary Louise Smith resigned as chairman, and he has failed to win unified support in his Midwestern region.

Buehl Berentson, 52, former executive director of the Republian Governors association. He is considered a competent technician, but lacks any substantial state base.

Arthur A. Fletcher, 52, a White House assistant and minority affairs consultant to the National Committee. Many Republicans have said since the 1976 election that the party has to do better with black vote to have a chance in national elections. The fact that Fletcher, a black, has yet to attract very much support indicates some of the difficulty the GOP has in accomplishing this objective.

The party's rules allow a candidate to be nominated if he has support from two persons in each of three states.