In 1998 Babula tied for 1st–4th with Liviu-Dieter Nisipeanu, Bartlomiej Macieja and Zoltan Almasi in the Zone 1.4 zonal tournament in Krynica and qualified to the FIDE World Chess Championship 1999 where he was knocked out in the first round by Tal Shaked. In 2007, he was joint winner of the Czech Open (with Viktor Láznička). He took part in the Chess World Cup 2011, but was eliminated in the first round by Zahar Efimenko.