If I understand correctly what you're trying to do, you're using the term "normalize" in a non-standard way. Conditional probabilities are already normalized in the sense that they add up to $1$.
I take it you want to map the relative frequencies observed in the text to conditional probabilities such that the relative frequencies in the closed interval $[0,1]$ are mapped to conditional probabilities in the open interval $(0,1)$. Note the plurals; you cannot just map one at a time as you seem to imply, since the conditional probabilities will not be conditional probabilities unless they add up to $1$, so their values have to be related.
Presumably the mapping should be monotonic in the sense that decreasing one relative frequency and increasing another should decrease and increase the respective conditional probabilities. In case by "infinitesimally close" you mean "arbitrarily close", the mapping cannot be done such that the resulting values get arbitrarily close to $0$ and $1$. This is precluded by monotonicity: The case where all relative frequencies are $0$ except one is $1$ has to be mapped to some conditional probabilities with a conditional probability less than $1$ corresponding to the relative frequency $1$, and by monotonicity no other set of relative frequencies can be mapped to a higher conditional probability than that.
However, if you merely wanted to allow, rather than require the conditional probabilities to get arbitrarily close to $0$ and $1$, there are many way to perform such a mapping. The most straightforward one would be to choose some monotonic function $f:[0,1]\to(0,1)$ and to define the conditional probabilities $p_i$ corresponding to the relative frequencies $\nu_i$ by
You could certainly use a sigmoid for $f$; I don't know of any "accepted" manner of choosing $f$.