Centering \vdots in a sparse matrix with an even number of rows

Two possibilities: the first one uses an additional column and the @{...} construct to decrease the inter-column spacing; the second one uses \tikzmark to place some marks and then places the \vdots using the marks.

\documentclass{article}
\usepackage{blkarray}
\usepackage{tikz}
\usetikzlibrary{calc}

\newcommand\tikzmark[1]{%
  \tikz[remember picture,overlay] \node (#1) {};}

\begin{document}

\[
\begin{blockarray}{cccc}
  \begin{block}{[c@{\hspace{3pt}}c@{\hspace{3pt}}c]l}
   &\vdots& \\
   a & & b & /K-1  \\
   c & & d & /K \\
  &\vdots& \\
 \end{block}
\end{blockarray}
\]

\[
\begin{blockarray}{ccc}
  \begin{block}{[cc]l}
   \tikzmark{a} & \tikzmark{b} \\
   a & b & /K-1  \\
   c & d & /K \\
   \tikzmark{c} & \tikzmark{d} \\
 \end{block}
\end{blockarray}
\]
\begin{tikzpicture}[remember picture,overlay]
\node[yshift=0.5ex] at ( $ (a)!0.5!(b) $ ) {$\vdots$};
\node[yshift=1.7ex] at ( $ (c)!0.5!(d) $ ) {$\vdots$};
\end{tikzpicture}

\end{document}

blkarray is able to do it without extra packages, just use \BAmulticolumn, which is the specific command for a blockarray:

\documentclass{article}
\usepackage{blkarray}

\begin{document}

\[
\begin{blockarray}{ccc}
  \begin{block}{[cc]l}
   \BAmulticolumn{2}{c}{\vdots} & \\
   a & b & /K-1  \\
   c & d & /K \\
   \BAmulticolumn{2}{c}{\vdots} & \\
 \end{block}
\end{blockarray}
\]

\end{document}