Machine Learning: Calibrating SubGroups of Probability Predictions inside a Dataset which should sum to 100%
Let $p_i=\Pr[F_i]$ be the probability that flower $i$ is a daffodil, according to your model (without taking into account the group structure).
Now you are given a group of 10 flowers, with probabilities $p_1,\dots,p_{10}$, and you're given the promise that exactly one of them is a daffodil.  To update your probabilities based on this additional promise, you can use Bayes rule.  Let $E$ be the event that exactly one in the group is a daffodil.    Then
$$\begin{align*}
\Pr[F_i|E] &amp;= {\Pr[F_i \land E] \over \Pr[E]}\\
&amp;= {\Pr[F_i \land E] \over \sum_j \Pr[F_j \land E]}.
\end{align*}$$
Note that
$$\Pr[F_i \land E] = \Pr[\neg F_1 \land \cdots \land \neg F_{i-1} \land F_i \land \neg F_{i+1} \land \cdots] = (1-p_1) (1-p_2) \cdots p_i \cdots (1-p_{10}) = {p_i \over 1-p_i} \prod_j (1-p_j).$$
Therefore,
$$\Pr[F_i|E] = {{p_i \over 1-p_i} \over \sum_j {p_j \over 1-p_j}}.$$
This is the probability you wanted to compute; so, use that.