Here is an application of a macro I showed in Aligning equations with left and right comment (you find there explanations).
\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand{\Prob}{\operatorname{\mathbb{P}}}
\newcommand{\tp}{\mathrm{tp}}
\newcommand{\fp}{\mathrm{fp}}
\newcommand{\fn}{\mathrm{fn}}
\newcommand{\tn}{\mathrm{tn}}
\newcommand{\Act}{\mathrm{Actual}}
\newcommand{\Pre}{\mathrm{Predicted}}
\newcommand{\Ar}{\mathrm{Accuracy}}
\newcommand{\Ps}{\mathrm{Precision}}
\newcommand{\Rc}{\mathrm{Recall}}
% the magic trick, see https://tex.stackexchange.com/a/209732/4427
\makeatletter
\newcommand{\Cen}[2]{%
\ifmeasuring@
#2%
\else
\makebox[\ifcase\expandafter #1\maxcolumn@widths\fi]{$\displaystyle#2$}%
\fi
}
\makeatother
\begin{document}
\begin{alignat}{2}
\Ar ={}& \Cen{2}{\Prob(\Act=\Pre)} &&= \frac{\tp+\tn}{N} \\
\Rc ={}& \Cen{2}{\Prob(\Pre=1\mid\Act=1)} &&= \frac{\tp}{\tp+\fn} \\
\Ps ={}& \Cen{2}{\Prob(\Act=1\mid\Pre=1)} &&= \frac{\tp}{\tp+\fp}
\end{alignat}
\end{document}
We need two groups of left-right columns, with no space between them, so I use alignat (the alignat* version will not print numbers). In the column we want centered, which is the second, I enclose the material as the second argument to \Cen (the first argument is the column number). We need &&= because the last column must be left aligned.

Note that the only real operator name is \Prob, the other symbols are just variables, so they should be defined with \mathrm. Note also \mid instead of |, which gives a better spacing.
Whether to center the second column is a judgment question; in my document I'd simply use gather or align to put the three equations flush left.
\begin{gather}
\Ar = \Prob(\Act=\Pre) = \frac{\tp+\tn}{N} \\
\Rc = \Prob(\Pre=1\mid\Act=1) = \frac{\tp}{\tp+\fn} \\
\Ps = \Prob(\Act=1\mid\Pre=1) = \frac{\tp}{\tp+\fp}
\end{gather}
\begin{align}
& \Ar = \Prob(\Act=\Pre) = \frac{\tp+\tn}{N} \\
& \Rc = \Prob(\Pre=1\mid\Act=1) = \frac{\tp}{\tp+\fn} \\
& \Ps = \Prob(\Act=1\mid\Pre=1) = \frac{\tp}{\tp+\fp}
\end{align}

eqnarraydoes not support anything other than two&in a line, your first example just generates errors???? – David Carlisle Nov 17 '14 at 19:44alignproduces different output thaneqnarrayby design. The spacing ineqnarrayis basically wrong. the spacing around=should not change just because the following line is aligned.eqnarraygives it the spacing fromtabularmore or less. – David Carlisle Nov 17 '14 at 19:46alignat:\begin{alignat*}{3} foo &= bar &&= baz \\ foobar &= barquux &&= bazzot \end{alignat*}. Please include an image of the output that you desire. – Peter Grill Nov 17 '14 at 19:47eqnarrayas the one defined in the latex format will generate an error on that input. so cannot guess what your output looks like – David Carlisle Nov 17 '14 at 19:47&taht's a highly hmm "inventive" use ofeqnarray:-) it absolutely was never designed to be used like that, the central column is supposed to be used for=or other operator on which to align, not whole subterms!. Also your example still is not a document that people can run. – David Carlisle Nov 17 '14 at 21:06