There is no such thing as "private" prayer. There is — and certainly should be — deeply personal prayer, but really no such thing as "private" prayer. All Christian prayer, if it is true to its name, is initiated by the promptings of the Holy Spirit received in Baptism, who prays in and through the hearts of the baptized who together are constituted as the Body of Christ, the Church. Two things are worth noting here: First, all prayer begins with God's initiative (it's graced — in the Tradition, the Holy Spirit is often referred to as "uncreated Grace"), and, second, the Church is constituted by God's action, not by mere human choice or conscious decision. Decision is obviously important, as the Gospels relate, in responding to Jesus, but it's also important to remember that the invitation comes first. All prayer then, personal or public, is done in communion with the Body of Christ, the Church, as the Spirit draws us in Christ to an ever-deeper communion with the Father.