The AI does not magically receive reinforcements out of nowhere, and have to abide by the same rules as the player. When declaring wars, you'll want to see how much money your enemy has. They will hire mercenaries if they need to and can afford it. This is generally the source of sudden bursts of troops on the opposing side that is not allies joining the war. You also want to consider if they can hire a Holy Order, this can also be a source of immediate reinforcements.
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