The probability is 1% during 2x.  Shards are a terrible value purchase imo. 

I only opened 3 void chickens so far, 2 dupe epics and a rare. 

How many quarters do I have to feed into a slot machine before I win the jackpot?

In the past, I've gotten 2 Void Legos in a single 10 pull...

In the past, I've pulled 50 Void Shards and gotten 0 Legos...

If you're going to buy shards... wait for a Guaranteed Legendary event. Anything you get before the Guaranteed Lego is just a bonus.

It took me more than a year to get my first ever void leggo. Bought a few small packs of shards in that time, maybe 20 total. I'm sure I popped well over 200 before hitting gold.

At least you got epics. :D So many times i pulled over 20 or 30 and was all rare. So frustrating when you watching the content creators videos on Ytube and see, they pulled from 20 void shards two top tier Void Legos. Just like Yst 2 weeks ago Yumeko and Marichka. LOL

So basically its a pain in the ass without events 

In general, the drop rates for rare items in games can be quite low, and even spending a lot of money does not guarantee that you will get the item you want. The drop rate for legendary items or other rare items in a game depends on the game's design and mechanics, as well as the developer's decision on how rare they want those items to be. Some games intentionally make rare items very difficult to obtain, even for players who spend a lot of money on in-app purchases. I often play games from https://joywallet.com/article/games-that-pay-real-money/ That way, I can make money and play at the same time. 

Watch for events where drop rates are doubled, but ignore the 10x ones.

My rates for voids at are very sad.  Not counting the recent guaranted, ive pulled 3 in 3 years, about 200 shards per year.  And two of those three where dups of crud champs!

Here's the deal.  RNG is RNG, right?  Some times you have good luck, sometimes it's bad.  I pulled Warlord with my very first Void shard.  Haven't pulled a single Void Leggo since.  That's just part of this game.  I get it, it's frustrating some times.  But I view Legendary Void Champs as a jackpot and Rares as the rule.  Now, I am F2P, I've been playing for 2 years, level 99, and am not endgame yet. I'm not 100% on the mechanics of the game itself, but I do understand the concept of chance.  I've hit on some solid leggos by chance early and recently, but inbetween was really touch and go for a while.

tl;dr-This is basically a game of chance when it comes to shard pulls.  expecting a leggo on voids or ancients is just generally a bad idea and will turn you off quickly.  make the most of what you get.