What is the ruling on distributing predatory animals captured from non-believers?

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If predatory animals like cheetahs or falcons are taken from non-believers, they are treated as divisible spoils of war. If they are dogs, selling them is not permitted. If no one desires them, they can be released or given away. If some desire them over others, they are given to them without being counted against their shares as they lack inherent value. If all desire them, they are divided by count if possible without valuation. If division is difficult or disputed regarding quality, lots are drawn.