China recently passed a law requiring games which offer randomized loot for money—like Hearthstone's card packs—to publish drop rates so that players know exactly how likely (or unlikely) they are to get rare items or cards.
Yesterday, Dota 2's publisher in China, Perfect World, published the drop rates for the rare items available in the Treasure of the Dota 2 Asia Championships 2017. That's the only Treasure currently available to purchase in China as Valve and Perfect World have taken the others off sale for now.
Regarding the Dota 2 Asia Championships Treasure, Eyes of the King has a 6 percent drop rate, and the Armor of the Shattered Vanguard has a 2 percent drop rate, if Google Translate can be trusted to get numbers right. (I especially love how Armor of the Shattered Vanguard becomes "disillusioned pioneer armor" by Google's estimation.)
These rates for rare items may only apply to this particular Treasure, and may not be the same everywhere outside of China—for all we know Perfect World has its own rates that differ from Valve's. But as more Treasures are added to the Chinese Dota 2 store and have their drop rates published, we may be able to make some deductions about how these items are handled outside of China.
Earlier this week, Riot published drop rates for League of Legends.