Babek qualified for the Czech squad in the men's team sprint at the 2008 Summer Olympics in Beijing by receiving one of the team's three available berths based on UCI's selection process from the Track World Rankings. Babek and his teammates Ptacnik and Spicka battled in an opening heat against the U.S. trio of Michael Blatchford, Giddeon Massie, and Adam Duvendeck with an eleventh-place time in 45.678 and an average speed of 59.109 km/h, failing to advance further to the top eight match round.