Prayer is by definition personal conversation with God.
Who’s definition is that?
Better stick with Church teaching:
WHAT IS PRAYER?
For me, prayer is a surge of the heart; it is a simple look turned toward heaven, it is a cry of recognition and of love, embracing both trial and joy.1
Prayer as God’s gift
2559 "Prayer is the raising of one’s mind and heart to God or the requesting of good things from God."2 But when we pray, do we speak from the height of our pride and will, or “out of the depths” of a humble and contrite heart?3 He who humbles himself will be exalted;4 humility is the foundation of prayer, Only when we humbly acknowledge that "we do not know how to pray as we ought,"5 are we ready to receive freely the gift of prayer. “Man is a beggar before God.”
2562 Where does prayer come from? Whether prayer is expressed in words or gestures, it is the whole man who prays. But in naming the source of prayer, Scripture speaks sometimes of the soul or the spirit, but most often of the heart (more than a thousand times). According to Scripture, it is the heart that prays. If our heart is far from God, the words of prayer are in vain.
2563 The heart is the dwelling-place where I am, where I live; according to the Semitic or Biblical expression, the heart is the place “to which I withdraw.” The heart is
our hidden center, beyond the grasp of our reason and of others; only the Spirit of God can fathom the human heart and know it fully. The heart is the place of decision, deeper than our psychic drives. It is the place of truth, where we choose life or death. It is the place of encounter, because as image of God we live in relation: it is the place of covenant.
http://www.vatican.va/archive/ccc_css/archive/catechism/p4s1.htm