Linkitch has provided a useful updated Patch 2.2 Legendary Drop Rates and Gambling Odds spreadsheet. You can download it or view it in Google docs, and the tables show all legendary and set items in the game, with 1) their odds to drop if a legendary item of that type rolls via smart loot, and 2) approximately how many blood shards you’ll need to gamble to obtain that item.The math is simple, since for every gear slot there are X number of items that can appear for each class, with a few of the items weighted to be less common than others. So if a Monk rolls a legendary bracer, there are 15 possible items that can fall, and a 9.30% chance that Gungdo Gear is the one selected by the RNG gods. The same theory works for every item in the game via drops.
Note that the drop odds apply only to smart drops, which are around 85% of item drops. About 15% are totally random, and can roll for your class or any other class. All gambling = smart loot though, so you’ll never gamble a legendary for some other class, or with a mainstat other than your character’s.
As more legendary items are added to the game, it grows harder to find any particular item, so your odds of finding the items in a specific set are probably a bit longer than before. It’s not all bad though, since Blizzard recently improved the odds of finding the most uncommon items, making most of them 1/4 as likely as others of their type, instead of the 1/10th chance they had before.
Thus if a Legendary two handed mace drops, the melee classes have a 4-6% chance of it being a Furnace (varies by class depending on how many different legendary 2H maces they can roll). The sticking point for most players is still the inability to gamble specific melee weapon types, so when you switch to the Gamble Weapons tab you see that it’ll take the melee classes 118,000 to 164,000 shards to have good odds of scoring a Furnace from Kadala. And there’s only a 1/10 chance that it rolls Ancient. Good luck with that!