The only son of composer Maurice Abrahams and singer Belle Baker, Herbert attended Yale School of Drama, receiving a Bachelor of Fine Arts.
Baker began his career in screenwriting in 1948 with Morgan's film debut So This Is New York, co-written with Carl Foreman and based upon Ring Lardner's 1920 novel The Big Town.
[2] He wrote Dream Wife (1953) with Sidney Sheldon for Cary Grant and Deborah Kerr, as well as several films for Dean Martin and Jerry Lewis such as Jumping Jacks (1951), Scared Stiff (1953), and Artists and Models (1955).
[4] Baker entered television writing and won Emmy Awards for An Evening With Fred Astaire in 1959 and The Flip Wilson Show in 1971.
[5] Baker wrote television scripts for many other singers such as Perry Como, Frank Sinatra, John Denver, Mac Davis and Gladys Knight & the Pips.