documentclass{article}
usepackage{pgfplots}
pgfplotsset{compat = newest}

newcommand{constant}{0.4}

begin{document}%
begin{tikzpicture}%
begin{axis}[%
             xmin = 0,
             xmax = 1,
             xtick = {0,constant}, % replace 0 by constant/(1 + constant)
             ymin = 0,
             ymax = 1
            ]%

addplot[domain = 0:1] {constant/(constant + x)};

end{axis}%
end{tikzpicture}%
end{document}%