Mark, putting it in laymans terms it can be as simple as looking at something and thinking ‘that should be favourite’ or ‘I don’t think that horse will win today why is it favourite’ blah blah etc etc.
My point is not to over complicate it initially whilst getting to grips with horse racing, the OP stated he was completely new to horse racing, it is best to learn about the sport first and foremost. If someone is mathematically minded they will either already understand math behind betting or pick it up very quickly.
We are on the same wave length with odds, there is plenty of information around these days to help starters and you are very forthcoming with newbies yourself which is great, keep it up, I was trying to make it a little easier for the OP seeing as he is only just dipping his toe into the water.
You see the maths as "complicat"ing things tb, I see it (once learnt) as simplifying. But it’s true we are on the same wave length. 
Fair enough, you might be right tb, a newbie doesn’t want to know the maths. It’s just that not knowing it got me in to bad habits that took time to unlearn once I did know my sums. 