... is basically the view with which most people operate. It is the belief that prayer changes things.
I don't personally believe that prayer can lead someone to become a Christian. That must ultimately be a matter of each individual. Can prayer make it more likely that someone will believe? I have serious questions about the goodness of such a possibility.
And to be sure, there are some bizarre features of prayer. God already knows what we need before we ask it (Matt. 6:8). In fact, we don't know exactly what we should pray for (Rom. 8:26). Why should we even pray?
The Calvinist view of prayer is that God has already determined the outcome of events before the foundation of the world. Prayer is simply one move in a chess game God is playing with himself. He causes us to pray as part of his predetermined plan to do something.
But an Arminian will probably see the "laws of prayer" as an opportunity God has given us to impact the flow of human events. It occurred to me this week that an Arminian might view prayer a little like I view God's relationship to the laws of physics. Sometimes two bits of metal are on certain trajectories at certain velocities and they crash into each other... and maybe I go to the hospital.
I don't see God always directing such events, although I believe he allows them. In the same way, perhaps God allows prayers or lack of prayers to affect the course of human events.
So perhaps sometimes God will do some things whether we pray or not. Perhaps sometimes God "quickens" some people to pray because he wants to give them an opportunity to catalyze the changing of things. And finally, God gives us the privilege to pray for our yearnings and requests in prayer. Perhaps sometimes he chooses to do such things, where otherwise he would not have.