Apologies Khandro, in attempting to remove complexity I've inadvertenty added a little. The amine radical is indeed NH2.
In summary, the 'blind watchmaker' analogy tempts the mathematician into making unnecessary calculations. The atoms in question have chemical characteristics pre-determined by their physical characteristics. They will tend to group together in certain ways. So to build up a probability profile based on randomness of atom A coming to rest beside atom B, then coming to rest beside atom C is entirely wrong. For example if you had just C, H and 2 Os in a sealed box and shook the box, maybe you would get COOH or maybe you would get COH with a spare O, but it doesn't matter, because in a short time it will become COOH all on its own. So the probability of that part of the event is 1. Just leave a glass of wine or beer for a few days and you will see.
The formation of amino acids, given an abundance of the necessary building blocks, water in its liquid state, various heat sources and maybe the odd lightning strike - was inevitable.