Petrásek, who started for the Dukla Liberec , ran in the World Cup for the first time at the 1988 Winter Olympics in Calgary . There he took 43rd place over 15 km classic and 32nd place over 30 km classic. In March 1988, in Rovaniemi , he took ninth place over 50 km in classic style, his first World Cup points. He had his greatest success at the World Championships in February 1989 in Lahti . There he won the bronze medal with the relay. In the individual races there he came in 37th place over 30 km classic and 18th place over 15 km classic. He also achieved his best individual result in the World Cup in the 1988/89 season with sixth place over 30 km classic in Nové Město and his best overall result in the World Cup at the end of the season with 23rd place in the overall World Cup. At the World Championships in 1991 in Fiemme Valley , he was tenth over 10 km classic, which was the last time he got World Cup points. He also achieved 41st place over 30 km classic and eighth place with the relay. The following year he ran at the Winter Olympics in Albertville to 66th place over 10 km classic, 55th place in the pursuit and 24th place over 30 km classic. In December 1993 he won the Continental Cup in Tauplitz over 15 km classic. At the 1994 Winter Olympics in Lillehammer , he won 71st place over 10 km classic and 58th place in the subsequent pursuit. In 1997 he won the König-Ludwig-Lauf classic over 55 km. He completed his 23rd and last World Cup race in January 1999 in Nové Město, which he finished classically in 78th place over 15 km.
In the Czechoslovak Championships Petrásek won three times over 30 km (1988, 1990, 1992) and once with the relay of Dukla Liberec (1991) and over 50 km (1987). In 1985 and 1986 he was Czechoslovak junior champion over 15 km.