Latex doesn't handle spacing around fractions inside arrays well. Get round this using, for example, \vspace{1 mm}, as follows:
\[ \left( \begin{array}{cccc}
\vspace{1 mm}
\frac{4}{9} & \frac{2}{9} & \frac{1}{9} & \frac{2}{9} \\ \vspace{1 mm}
\frac{2}{9} & \frac{4}{9} & \frac{2}{9} & \frac{1}{9} \\ \vspace{1 mm}
\frac{1}{9} & \frac{2}{9} & \frac{4}{9} & \frac{2}{9} \\ \vspace{1 mm}
\frac{2}{9} & \frac{1}{9} & \frac{2}{9} & \frac{4}{9} \\
\end{array} \right)\]
It's still not quite right, but is better than default.
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