As early as in the 1960s, Gottfried Michael Koenig developed computer programs Project 1 and Project 2 for aleatoric music, the output of which was sensibly structured "manually" by means of performance instructions.

Who invented generative music?

Brian Eno, who coined the term generative music, has used generative techniques on many of his works, starting with Discreet Music (1975) up to and including (according to Sound on Sound Oct 2005) Another Day on Earth.

When did Lejaren Hiller created a computer program that could notate music by applying calculations of probabilities based on traditional musical rules?

The earliest instance of computer generated composition is that of Lejaren Hiller and Leonard Isaacson at the University of Illinois in 1955-56.