Avoiding to go into the mathematical complexities that one could go into here, the expression

$P(A)$ essentially is a shortcut for $P(\{A\; {\rm is\; realized\}})$. Moreover $P(A) = 1$ is equivalent ("almost surely") to $\{A\; {\rm is\; realized\}}$.

So

$$P(P(A) = 1) = P(\{A\; {\rm is\; realized\}}) = P(A)$$

Of course, unending discussions and explorations can arise if one wants to discuss issues of objective/subjective probability, measure theory etc.

Avoiding to go into the mathematical complexities that one could go into here, the expression

$P(A)$ essentially is a shortcut for $P(\{A\; {\rm is\; realized\}})$. Moreover $P(A) = 1$ is equivalent ("almost surely") to $\{A\; {\rm is\; realized\}}$.

So

$$P(P(A) = 1) = P(\{A\; {\rm is\; realized\}}) = P(A)$$

Of course, unending discussions and explorations can arise if one wants to discuss issues of objective/subjective probability, measure theory etc.

ADDENDUM
Responding to a comment by the OP, the verbal statements surrounding the $0.8$ number are both too vague in order for anything respectably "definite" to be said about them or their relation. Admittedly, they do sound different: one could argue that the first one is closer to an expression of an estimated objective probability, while the second, more personalized and categorical in tone, leans more towards an expression of a subjective degree of belief.