With your code, the easiest option would be to use a tabular and manually label each figure inside it.
\documentclass{article}
\usepackage{graphicx} % Required for including images
\usepackage[font=small,labelfont=bf]{caption} % Required for specifying captions to tables and figures
\begin{document}
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=0.49\linewidth]{example-image-a} &
\includegraphics[width=0.49\linewidth]{example-image-b} \\
a) & b)\\
\end{tabular}
\captionof{figure}{Probability distribution with loading level of a): 0.8 ; b) 0.9}
\end{center}
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=0.49\linewidth]{example-image-a} &
\includegraphics[width=0.49\linewidth]{example-image-b} \\
a) & b)\\
\end{tabular}
\captionof{figure}{Probability distribution with loading level of a): 1.0 ; b) 1.1}
\end{center}
\end{document}

Although I think it's better to use subfigure environments from subcation package. They help to manage automatic references and better align subfigures and captions.
\documentclass{article}
\usepackage{graphicx} % Required for including images
\usepackage[font=small,labelfont=bf]{caption} % Required for specifying captions to tables and figures
\usepackage[subrefformat=parens]{subcaption}
\begin{document}
\begin{figure}
\begin{subfigure}[b]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{First}\label{fig1a}
\end{subfigure}\hfill
\begin{subfigure}[b]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{example-image-b}
\caption{Second}\label{fig1b}
\end{subfigure}%
\caption{Probability distribution with loading level of \subref{fig1a}: 0.8 and \subref{fig1b}: 0.9}
\end{figure}
\begin{figure}
\begin{subfigure}[b]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{example-image-b}
\caption{First}\label{fig2a}
\end{subfigure}\hfill
\begin{subfigure}[b]{.49\linewidth}
\centering
\includegraphics[width=\linewidth]{example-image-a}
\caption{Second}\label{fig2b}
\end{subfigure}%
\caption{Probability distribution with loading level of \subref{fig1a}: 1.0 and \subref{fig1b}: 1.1}
\end{figure}
\end{document}
