A language is in $\mathsf{Almost\text{-}PSPACE}$ if there is a (deterministic) $\mathsf{PSPACE}$ Turing machine with an oracle $A$ that accepts the language with probability $1$ when the oracle language is chosen uniformly at random [1,2]. (That is, the language accepted by the oracle is determined by tossing a fair coin for each possible string.)
I can't understand the difference between $\mathsf{Almost\text{-}PSPACE}$ and $\mathsf{IPP^A}$.
Is it possible that $\mathsf{P} = \mathsf{PSPACE} \subsetneq \mathsf{Almost\text{-}PSPACE}$? Or, maybe it is already known that $\mathsf{P} \subsetneq \mathsf{Almost\text{-}PSPACE}$? Or it will imply that $\mathsf{P} = \mathsf{Almost\text{-}P} = \mathsf{Almost\text{-}PSPACE}$?
[1] Complexity Zoo.
[2] C.H. Bennett and J. Gill, Relative to a random oracle $A$, $\mathsf{P}\neq\mathsf{NP}\neq\mathsf{co\text{-}NP}$ with probability $1$. SIAM Journal on Computing, 10(1):96–113, 1981. (Paywalled PDF.)