According to I Kings 3, God appeared to Solomon in a dream and told him to ask for anything he wanted.
Solomon told the Lord that he wanted wisdom to govern his people and discern right from wrong.
God told him since he asked for this and not riches or a long rule, God would give him all three things. The story you are referring to immediately follows this text.
If you will notice, the text does not say that Solomon prayed about this decision, but that the wisdom had been given to him by God. (Verse 28)