[1] Following his graduation from National University, Hincapié was hired as the Secretary of Public Works for the municipality of Bello, Antioquia, for about eight months.
[1] In 1977, Governor Sierra, with the approval of Colombian President Alfonso López Michelsen, appointed Hincapié as the new Mayor of Medellín.
[1] Hincapié received the appointment just two days after speaking with President López Michelsen at the opening of the 1978 Central American and Caribbean Games in Medellín.
[1] His wife of six decades, prominent Colombian professor and sociologist María Teresa Uribe, died six days later on January 1, 2019.
[3] They were survived by their three children: Luis Guillermo, a civil engineer, Ana Lucía, a physician, and Marta Hincapié Uribe, a filmmaker and academic.