"For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren. Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified." (Romans 8:29-30)
"Having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will ... In whom also we have obtained an inheritance, being predestinated according to the purpose of him who worketh all things after the counsel of his own will" (Ephesians 1:5, 11)
"Before I formed thee in the belly I knew thee; and before thou camest forth out of the womb I sanctified thee, and I ordained thee a prophet unto the nations." (Jeremiah 1:5)
"And now, saith the LORD that formed me from the womb to be his servant..." (Isaiah 49:5)
"Nevertheless the solid foundation of God stands, having this seal: “The Lord knows those who are His,” (2 Tim. 2:19)
I totally believe God knows who He is going to call before we are formed in the womb. When I think on this fact and realize how I've been saved by Jesus Christ, I'm completely humbled. I started weeping the first time I thought about it. God has no favoritism (Galatians 2:6), but He does know whose are His, and those He is going to choose. If one believes that the Father chose Christ's disciples, they at least believe somewhat in predestination.
The deeper question is, why God chooses people like Judas and Pharoah to be decieved and hardened and walk the path of destruction? I don't understand it, but God raises up kings and brings them low (Daniel 2:21), and I can only be thankful that I'm in Christ.