This vocabulary connection is unusual, but strikingly logical. When you are prostrate with grief, you feel suppressed, overcome by the emotion. Your energy has been deprived of its force, and it is at its lowest. When physically prostrate, your body is at the lowest earthly position it can occupy.
How does a word change its meaning? What occurred in the year 1651 that catalyzed the shift in etymology from a physical arrangement to an emotional affliction. According to my research, the English civil war ended in 1651, in the scholarly period known as the Age of Enlightenment. Perhaps in this period of peace and self-reflexiveness, individuals were able to draw the connection between spatial arrangement and emotions. The emergence of this specialized way of thinking is seen in the adoption of jargon from popular writings at the time, such as Hobbes' Leviathan.
King's College Library in Cambridge, UK