Why does not current flow in open circuit wire connected to a closed circuit?
I have no idea whether this will help you or anybody else but your question, "I was wondering why it does not flow towards point "a" and why isn't it divided into "i_y" and "i_x"?" makes me think that you imagine that the 'a' branch can accept current.

If I can use a road and traffic analogy it might look like this:



Figure 1. Top: open circuit. Bottom: closed circuit.

As Figure 1 attempts to show, the whole road network is full of cars. When the switch is closed and traffic is allowed to flow all the vehicles in the closed loop align and begin to circulate. None branch down the dead-ends as there is no room and no way out for the vehicles. (The main circuit is already full and can't take vehicle from one of the dead-ends.)

You could make similar analogies with water pumps, etc., but the important thing to realise is that the system is already primed. There are no voids for "current to flow into".