Kubálek had first piano lessons with Otakar Heindl and was then 1952-1957 student of Oldrich Kredba at the Prague Conservatory and up to 1959 by Zdeněk Jílek at the Music Academy. From 1961 to 1968 he taught at the Prague Conservatory, performed in concerts and on the radio and played records on a Supraphon.
In 1968 he emigrated to Canada and became a Canadian citizen six years later. In 1969, he debuted in the Walter Hall, University of Toronto, and had shortly afterwards his first appearances with the Toronto Symphony Orchestra. It was followed by numerous radio recordings and live performances with other orchestras, the Vághy and the Orford String Quartet and as a companion to musicians like Victor Brown, Lois Marshall and Roxolana Roslak.
In the years 1974 to 1975, he led the St Paul's Centre in Toronto complete Mozart sonatas. Among other things, he played premieres of works by Walter Buczynskis, Ka Nin Chan, Paul Kilburns, Rudolf Komorous ', Milan Kymlicka, Marjan Mozetichs, Norman Sherman and Peeter Tammearus. Glenn Gould produced with him a recording of Sonata No.. 1 of Erich Wolfgang Korngold. For the bicentenary of the United States, he took an LP on her own arrangements of compositions by John Philip Sousa. Since 1986 he works as a pianist, producer and author of liner notes for Dorian Records.
Kubálek taught from 1969 to 1975 at the Brodie School of Music and Modern Dance in Toronto and gave 1975 and 1976 summer courses at the School of Music Blue Mountain in Collingwood. From 1979 he was a teacher at the Royal Conservatory of Music of Toronto and later at the University of Toronto ( 1996-2002) and York University (1997-2002 ).
In 1991 he joined the first time since his emigration again in Czechoslovakia. During his appearance during the Prague Spring in 2002 at the Rudolfinum, the home of the Czech Philharmonic in Prague, he was celebrated with standing ovations. In 2003 he founded the Kubálek International Piano Courses, a festival for young pianists, which takes place annually in Zlaté Hory.