Thank you all for your advice and kind words.

I went to the CID section of traffic police today. Turned out that it was just a minor driving violation. I was fined 500 riyals which I paid and that was it.

Unfortunately, again it was explained to me in Arabic so I could not understand much. I think kevin86 is correct that for some driving violations penalty amount is not fixed and that is why it stays with CID. If serious, the case may go to court. My case was simple so they closed it right there.

My advise to everyone, drive safely. Doha is a small city. By driving fast or dangerously, you may save 5 or 10 minutes so you have to ask yourself, is it really worth it.