After the National Dex.
A Heart Scale is uncommon.
As of 2023, there’s still no known percentage for the Underground Items.
Source
Serrebii.net says its "uncommon" which means basically rare. So im going to say about 10% chance but I cant be sure.
Each item has a respective appearance rate, which depends on game version (DP) or the player's Trainer ID number (Pt) and on whether the player has obtained the National Pokédex. Appearance rates work like a lottery system, where the rate is the number of lottery tickets an item has in the pot. For example, an item with a appearance rate of 15 is 3× more likely to be selected than another item with an appearance rate of 5. The exact likelihood for an item to be selected is its appearance rate divided by the sum of all appearance rates in the same list. In practice, item rarity is more complicated. First, an item is selected from the appropriate list, weighted by appearance rate. Next, an attempt is made to place the item in a random spot on the mining grid. This attempt fails if the item would partially hang outside the grid area or overlap with a previously-placed item. If this happens, the process starts over by selecting a random item from the list again. Large items like the Root Fossil will fail to be placed more often than small items like the Heart Scale, and therefore they will be less common than their appearance rate alone would indicate.
Each item has a respective appearance rate, which depends on game version (DP) or the player's Trainer ID number (Pt) and on whether the player has obtained the National Pokédex. Appearance rates work like a lottery system, where the rate is the number of lottery tickets an item has in the pot. For example, an item with a appearance rate of 15 is 3× more likely to be selected than another item with an appearance rate of 5. The exact likelihood for an item to be selected is its appearance rate divided by the sum of all appearance rates in the same list.
In practice, item rarity is more complicated. First, an item is selected from the appropriate list, weighted by appearance rate. Next, an attempt is made to place the item in a random spot on the mining grid. This attempt fails if the item would partially hang outside the grid area or overlap with a previously-placed item. If this happens, the process starts over by selecting a random item from the list again. Large items like the Root Fossil will fail to be placed more often than small items like the Heart Scale, and therefore they will be less common than their appearance rate alone would indicate.
Pre-National Pokedex, Heart Scales have an appearance rate of 33 in all games. Post-National Pokedex, it becomes 30. This means they're more common than most of the items available and advantaged by their small size, which allows them to fit the mining grid more often.
Underground (Bulbapedia)
