It's not...unless we serve a God who can do anything, including the ability to determine the impact prayer will have on the direction and execution of His will. In other words, only a sovereign and all-powerful God can choose to allow the prayers of sinful human beings to have an impact on His determined will.
Theologians, Bible scholars and just plain Christians have been pondering and debating this question for a long time. But the problem with addressing ourselves to the understanding of God and how He works among the sons of men is that we have a very limited understanding. Even the Apostle Paul—who understood a lot—had to stop and say:
Oh, the depth of the riches of the wisdom and knowledge of God! How unsearchable his judgments, and his paths beyond tracing out! "Who has known the mind of the Lord? Or who has been his counselor?" Romans 11:33-34 (NIV)
The simple answer is that how prayer works is beyond our ability to comprehend. But Pastor Chuck Smith used to say that when we are faced with things we don't understand, we should fall back on what we do understand. So here's what we know about prayer. God's Word tells us:
1. ...to pray. (2 Chronicles 7:14)
2. ...that God will hear us (2 Chronicles 7:14)
3. ...that prayer makes a difference (James 5:16)
The details are bound up in the wisdom and majesty of God and, for now, we will just need to leave them there.