Randomly picking a real number - chances the result is irrational?

Someone posted a similar question posted to r/theydidthemath that made me wonder this:

Of course it’s a common tidbit that the chances of picking an integer on a real number scale are 0.

But taking it a step further, what are even the chances of picking a rational number? Also 0?

What about the chances of picking an irrational number? Can you actually say the chances of an irrational number are 100%?

If the number can have infinite digits and decimals, but with no definitive way to calculate them (like irrational roots) how can you say the number will definitely be irrational?