# Containment: deterministic versus with probability one

As I was browsing the Complexity Zoo, I came across this statement:

Relative to a random oracle, PH is strictly contained in PSPACE with probability 1 [Cai86].

What confused me was the addition of "with probability 1". What does that mean and why is the current formulation different from

Relative to a random oracle, PH is strictly contained in PSPACE [Cai86].

A related question: is there a difference between saying something is deterministic or some process succeeds with probability one?

Edit: as pointed out in the comments, a correct example distribution would instead be a uniform distribution over $$[0,1]$$. A number selected from this distribution is non-zero with probability 1, but not all numbers in this distribution are non-zero.
• @EmilJeřábek Just switch his example to uniform distribution on $[0,1] \subseteq \mathbb{R}$. Jul 7 at 13:15