Assuming a 385 day maleh leap year in Diaspora and no Torah portions doubled which would yield 54 Shabbatot.
Every day of the year has, Ma'ariv, Shacahrit and Mincha. Including both silent & repetitions you get 5 Amidot per day.
385 * 5 = 1,1925
Add an extra 2 for the days of Musaph:
54 Shabbatot + 20 days Rosh Hodesh + 22 Yom Tov = 96 days * 2 Amidot ...
This question is in fact dealt with by Rashi on the spot, who says that the first ה is redundant, and this has the same meaning as מלך המשפט, citing scriptural precedents for this phrasing. Basically - this is an unusual, anomalous usage which חז"ל chose for some reason, but the normative way of saying this would be מלך המשפט - king of justice.
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