Hm, quite unusual demand. Your wish require manual tweaking of equation positioning, for example with use of the \phantom
macro:
\documentclass[a4paper,12pt]{article}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\usepackage{amsmath}
\begin{document}
\begin{align*}
0.01 & = 1 - P(Z_i<c_1)\\
\hphantom{1 - P}(Z_i<c_1) & = 0.99
\end{align*}
\begin{align}
0.01 & = 1 - P(Z_i<c_1)\\
\hphantom{1 - P}(Z_i<c_1) & = 0.99
\end{align}
\end{document}

(red lines shows text borders)
or use the following unusual construction of nonnumbered equation system writen in tabularx
table:
\documentclass[a4paper,12pt]{article}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%
\usepackage{amsmath}
\usepackage{tabularx}
\newcolumntype{L}{>{\raggedright\arraybackslash$}X<{$}}
\newcolumntype{R}{>{\raggedleft\arraybackslash$} X<{$}}
\begin{document}
\[\setlength\tabcolsep{2pt}
\begin{tabularx}{\linewidth}{R >{$}c<{$} L}
0.01 & = & 1 - P(Z_i<c_1) \\
(Z_i<c_1) & = & 0.99
\end{tabularx}
\]
\end{document}

align
if you don't want thigns aligned. Trygather*
instead.alignat
.