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In Pokemon Ruby, what would the odds of finding a single Rare Candy be after one battle if I have a team of 5 Zigzagoon with Pickup? In Ruby version, Pokemon with Pickup have a 10% chance of finding an item after battle. There is a 10% chance that item is one of eight specific items. One of these eight items is a Rare Candy. If I have 5 Zigzagoon, what would the odds of finding a Rare Candy be? 1/10 x 1/10 x 1/8 x 5? Thanks!

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What level are the Zigzagoon? Level influences what items are found as well. :P
@Jack First, do you want the chance of finding at least 1 rare candy or exactly 1 rare candy? Second, who told you that's how pickup worked? Bulbapedia says it's 10% chance to find any item, and of those 10%, 10% are rare candies. So the chance of finding a rare candy with 1 Zigzagoon is 1%. https://bulbapedia.bulbagarden.net/wiki/Pickup_(Ability)
@Stakataka Level affects pickup only from Emerald onward.

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The odds of finding an item at all is 10%, then the odds of that item being a Rare Candy is 10% on top of that, so each Zigzagoon has a 1% chance of finding a Rare Candy (1/10 * 1/10 = 1/100). I checked Bulbapedia, and I don't know where you're getting the 1/8 from.
Finally, the culminative chances of finding a Rare Candy after 5 independent Zigzagoons will not be exactly the same as just multiplying this by 5 (for the same reason why you're not guaranteed to get a shiny even after 4096 encounters), so just trust me when I say that the chances are 4.900995% per battle (assuming all Zigzagoons have no item before each battle). (It's practically 5% anyway, so I honestly don't know why I went through all this for effectively the same answer...)

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Just to be clear, 0.049 is the chance of getting at least 1 rare candy after each battle. Because sometimes you get more than 1 rare candy, the average number you get after each battle is 0.05.