Let's define $PP_c$ as a set of languages: A language $L$ is in $PP_c$ iff there exists a polynomial $p: \mathbb{N} \rightarrow \mathbb{N}$ and a polynomial time turing machine $P$ s.t. if $x \in L$ then $Pr[P(x, u) = 1] \geq c$ and if $x \notin L$ then $Pr[P(x, u) = 1] < c$, where $u \in \{0,1\}^{p(|x|)}$. I have learned that $PP = PP_{0.75}$, other sources define $PP = PP_{0.5}$.
Does $PP = PP_c$ hold for every $0 < c < 1$? Or what are adequate restrictions for $c$ s.t. $PP = PP_c$?