I was thinking about the chance of get a legendary engram and earn a legendary item when figured out how the drop chance is low, but nothing compared with the drop chance plus the engram chance of earning the desired item.
If you read on some posts, you'll notice the chance of at least 1% of purple engram dropping, the same for earning a legendary item from this engram, so, let's calculate the chance of earning a legendary item:
0,01 (1%) * 0,01 (1%) = 0,0001 (0,01%) or 1 in 10.000 drops.
It's not saying the earned item is the desired item, so, you'll need to divide it with all the slot type of equipment and then divide again with all the legendary items inside that slot type.
0,0001 / 7 Slot Types / 30 (random number of legendary items of that type) = 0,000000476 (0,0000476%) or 1 in 47.600.000 millions.
It's a chance, even if you kill 47.600.000 monsters, your chance of drop one purple engram still attached with the probability of never earning the desired item.
Well, I don't want complain about it, just want show for you how hard is your chance of earn the desired item is at least a real lottery.