Let's say I use a music in my video, which I upload to youtube. What are the chances (probability) that the copyrightowner will contact youtube and my video will be muted?
Are there any kind of statistics on this?
If there is - what are this probability depends on?
It's hard to say. In my experience, copyright analysis is near real time, and my experience has been that the algorithm identifies and blocks copyrighted material in minutes. No one needs to contact YouTube.
Most copyright holders simply monetize your video, meaning ads will be shown and they get the advertising revenue. Others will block it until you blank out the offending material.