In God's will of Purpose, He had chosen Pharaoh as a tool to bring about the deliverance of Israel from Egyptian bondage (Exodus 9:16). In His Foreknowledge, God told Moses that "I am sure that the king of Egypt will not let you go" (Ex. 3:19; 4:21). The hardening of Pharaoh's heart is foretold, as well as the hardening of the hearts of the Egyptians (Ex. 14:17).
Pharaoh also hardened his own heart in response to God's dealings with him regarding the release of Israel (Ex. 8:15,32; 9:34). So, Pharaoh's heart was providentially hardened, but also personally hardened. Providentially, God hardened Pharaoh's heart in order to complete His purpose - but Pharaoh could have humbled his heart by choice - therefore, his hardness grew even greater.
Hard hearts are the real problem in relationships between God and man, and between man and his fellow man, and between parents and children, and between husbands and wives, etc. We have a choice.
Jesus told the disciples that the reason Moses gave a law concerning divorce was due to 'hardness of hearts" (Matt. 19:8). How true! Hardness of hearts towards others is the underlying cause for our 'people problems'.
Unbelief also results in hardness of hearts (Mark 16:14). Like physical heart conditions, spiritual hardness of the heart must be treated. A changed heart (Ezekiel 11:19; 36:26), a spiritual heart transplant, as it were, results in a renewed heart.
The work of the Spirit and the Word of God make up the spiritual surgical team that can perform this operation.
Think about this as you sing, "Into my heart, Into my heart; Come into my heart, Lord Jesus..."