The conflict that arises after the first set of prophecies come true is both internal and external for Macbeth. Internally, the prophecy unleashes a struggle within himself, he lusts for power, and his ambition to possess that power is set in motion. He begins to ponder how he can obtain the power promised in the prophecy, but he wants it now. So he considers committing murder, killing King Duncan.
He goes through many stressful internal discussions with his conscience to determine whether he has the true nature to commit murder.
"When Duncan announces that his son Malcolm will succeed him as king, Macbeth outwardly supports Duncan’s decision. However, he is disappointed and knows he must eliminate Duncan and his son Malcolm to become king. Macbeth now struggles with this conflict and ponders what fate may bring."
His external conflicts arise first with King Duncan, who is in his way if he wants to sit on the throne, also Malcolm and Donalbain, the sons of the king are also in his way.
Additionally, Macbeth has a conflict with his wife, once she learns of the witches prophecies. She becomes drenched in the desire to be queen. She ridicules, humiliates and uses her feminine wiles to convince her husband to commit murder when the king arrives for his visit at their home.