Your are right with ARD and ZDF. But Channel 3's are local TV stations.
Every federal state in germany has it's own channel.
For example: channel 3 in Bavaria is called "BR Fernsehen", channel 3 in Baden Württemberg is called "SWR Fernsehen", and so on.
This is from a time when there were only three television channels in Germany, ARD, ZDF and "Drittes".