What properties does a co-RP problem need to be in P? Given an arbitrary language $L$ with an algorithm $A$ that places $L$ in $co-RP$ what other properties does the Algorithm $A$ need to have to so that $L$ is in $P$?

For example:

Considering $L$ is in $co-RP$ we have a guarantee that:

if $x \in L$ then $A$ accepts $x$ guaranteed $(P(A(x)=1) = 1)$

if $x \not\in L$ then $A$ accepts $x$ with a propability $f(n)$ $(P(A(x)=1) = f(n))$ with $n = |x|$ and $f(n) \geq 0$

What property does $f$ need to have so that $L$ is in $P$?

As $P \subseteq ZPP$ and $ZPP = RP \cap co-RP$ there needs to be a property to $f$ that places $L$ also in $RP$. As such there needs to be a way to construct an algorithm $B$ for $L$ that discards $x \not\in L$ guaranteed in polynomial time. Under what conditions for $A$ is this possible? For what $f$ is this the case? Is there any other property $A$ needs to have so that $L$ is in $P$?
Considering from my comment that there exists an upper bound to the runtime of $A$: $p(n)$ then there are only $2^{p(n)}$ possible ways a coin-flip of a randomized algorithm can manipulate the outcome of the result.

If the error propability of $A$ I described as $f$ is a fraction with part $\frac{g(n)}{2^{p(n)}}$ then creating a deterministic program that runs $g(n)$ many times plus one different paths of a possible computation of $A$ it is guaranteed that at least one of these paths would have identified the false positive as false.

Therefore we can skip the journey through $RP$ into $ZPP$ and can argue that if $g$ is a polynomial function we need to run $g(n) + 1$ times the polynomial Algorithm $A$ resulting in a polynomial runtime of $(g(n)+1) \cdot p(n)$ that deterministically solves $x\in L$ or $x \not\in L$ with an error propability of $0$, therefore placing $L$ in $P$.

This is but one case where, given a randomized algorithm that places a language $L$ clearly in $co-RP$ places $L$ also in $P$.