24 decks

First, let us consider one deck. We don't care where the Ace through 4 of hearts appear in the deck, so long as they appear in the right order. There are $4! = 24$ possible orders for these four cards, and only one of them is acceptable. So the probability of one deck having those four cards in order is $\frac{1}{24}$ and the probability of those cards being out of order is $1-\frac{1}{24}=\frac{23}{24}$ .

Thus, the probability of none of our 24 decks having the desired order is $\left(\frac{23}{24}\right)^{24}$ . Finally, the probability that at least one deck has this order is $1-\left(\frac{23}{24}\right)^{24}\approx \boxed{0.64}$