Prokop made his WRC debut at the 2005 Monte Carlo Rally in a Suzuki Ignis S1600, competing in the Junior World Rally Championship category. In 2006 he claimed his first JWRC category win at Rally Catalunya in a Citroën C2 S1600, finishing tenth in the JWRC standings overall that season.
In 2007 Prokop became more competitive, winning both the Rallye Deutschland and the Tour de Corse in the JWRC category and placing third in the overall JWRC standings behind Per-Gunnar Andersson and Urmo Aava. For 2008, Prokop contested both the JWRC and the Production World Rally Championship simultaneously, finishing third in JWRC and fifth in the PWRC.
The 2009 season brought Prokop his most significant achievement. Driving a Citroën C2 S1600, he won the JWRC categories at Rally Cyprus and Rally Italy before clinching the Junior World Rally Championship title with a victory at Rally Finland in August. He simultaneously finished second in the 2009 PWRC standings, behind Armindo Araujo.
In 2010, Prokop moved to the Super 2000 World Rally Championship with a Ford Fiesta S2000, entered by the Czech Ford National Team. He became the first driver to win a WRC special stage in an S2000 car, taking SS16 at the 2010 Rally Sweden. He followed with third place at Rally Sweden, second at Rally Mexico, second at Rallye Deutschland, and second at Rally Japan. A title shot evaporated at the Rallye de France when power steering problems cost him time across every stage; he finished sixth and lost the SWRC title.
Prokop stepped into the full World Rally Championship with the Czech Ford National Team in a Fiesta RS WRC from 2012. That season he finished ninth in the WRC standings with 46 points, taking his best finish of fourth in Argentina. In 2013, now with the Jipocar Czech National Team, he again placed ninth with 63 points, with another fourth-place finish at Rallye Deutschland representing his best result. He retained ninth in 2014 with 44 points and fell to eleventh in 2015 with 39 points, again achieving a fourth place at Rally Argentina.
In 2016, Prokop entered the Dakar Rally — his debut at the event — competing alongside fellow WRC professionals Mikko Hirvonen and Sébastien Loeb, both also on their Dakar debuts. He returned to WRC mid-year, finishing seventh at Rally Mexico.
Prokop made limited WRC entries from 2017 through 2020. In 2021 he drove an M-Sport Ford Fiesta R5 Mk.II. From 2022 onward he entered events in his own Fiesta Rally2, continuing to appear in WRC rounds through 2025, when he made three starts and finished sixteenth in the championship standings. His career total across the WRC stands at 145 starts, with a best finish of fourth and 310 points accumulated.
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