All six qualifiers take place over the next few months, with automatic qualification or a play-off place determined by November.
Scotland's only defeat in the previous World Cup qualifying campaign came in Copenhagen, with the Danes topping the group by four points.
As runners-up, Clarke's side were then denied in a play-off semi-final at home to Ukraine.
The former West Bromwich Albion, Reading and Kilmarnock manager admits it's a challenging group, predicting a tight race.
"Three good sides," he said. "Denmark are obviously an established pot one team. They've been known to get to the later stages of tournaments.
"We saw Greece at Hampden in March [a 3-0 defeat]. We know they're a good team and they're probably a team that's on the ascendancy, coming up the way.
"So they're maybe one of the more difficult pot two teams and Belarus are a strong pot four team. We know it's a tough section where the teams can all take points off each other.
"It's another opportunity. It's a tournament we haven't been at for a long, long time.
"We believe that this group of players and this group of coaches can deliver, so that's what we have to try and do."