Psalm 119:148 Mine eyes prevent the night watches, that I might meditate in thy word
Prayer is converse with God; the intercourse of the soul with God, Prayer may be oral or mental, occasional or constant, ejaculatory or formal.
Around that time everything is very quiet and your attention will be high.
(Mat 6:5-6 KJV) 5 And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray to stand in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward.
6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
The regular times of prayer were the third (morning sacrifice), sixth, and ninth hours (evening sacrifice):
Psalm 55:17 Evening, and morning, and at noon, will I pray, and cry aloud: and he shall hear my voice
Acts 2:15 For these are not drunken, as ye suppose, seeing it is but the third hour of the day
Psalm 119:147 I rise before dawn and cry for help; I have put my hope in your word.
Praying that time is fine to the person praying because 3:00 am is just a normal time that one praying will have time to meditate and concentrate Anytime is good for prayers but around that time many are asleep and you can have time to concentrate on what you are saying.