How can I convert the probability score between 0 to 1 to another format? I have trained a multi-class CNN model using fastai. The model splits out probabilites for each of the three classes, which, of course, sum up to 1. The class with highest probability becomes the predicted class. 

Is there any way I can convert them into 0 to 1 scale, where near to 0 value would mean class 1, near to 0.5 would mean class 2 and near to 1 would mean class 3?
You could maybe do something like this, it's a bit hackish
\begin{equation}
y = C_1\cdot 1 + C_2 \cdot 0.5 + C_3 \cdot 0
\end{equation}
$y$ represents the output and its bounded $\in [0, 1]$. $C_i$ is probability for class $i$. This way when $C_1 \approx 1, C_2 \approx 0, C_3 \approx 0$ you have
\begin{equation}
 y \approx 1\cdot 1 + 0.5 \cdot 0 + 0 \cdot 0 \approx 1
\end{equation}
when $C_1 \approx 0, C_2 \approx 1, C_3 \approx 0 $ you have
\begin{equation}
 y \approx 1\cdot 0 + 0.5 \cdot 1 + 0 \cdot 0 \approx 0.5
\end{equation}
and when $C_1 \approx 0, C_2 \approx 0, C_3 \approx 1 $ you have
\begin{equation}
 y \approx 1\cdot 0 + 0.5 \cdot 0 + 0 \cdot 1 \approx 0
\end{equation}