Paradox Brownian Motion : P(first passage time < infinite) = 1 yet E(first passage time) = infinite?

Question

I am studying the bible of stochastic calculus for finance by Shreve aka God.

But in the section "first passage time to level m" for the Brownian Motion there is a paradox :
1) P(first passage time < infinite) = 1
2) E(first passage time) = infinite

For me it is a paradox. How can you be at the same time finite and infinite?

Is there a solution or a interpretation to solve the paradox ?

Thanks