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In this paper, we present a practical implementation of the parametric multi-channel Wiener filter (PMWF) noise reduction algorithm. In particular, we extend on methods that incorporate the multi-channel speech presence probability (MC-SPP) in the PMWF derivation and its output. The use of the MC-SPP brings several advantages. Firstly, the MC-SPP allows for better estimates of noise and speech statistics, for which we derive a direct update of the inverse of the noise power spectral density (PSD). Secondly, the MC-SPP is used to control the trade-off parameter in PMWF which, with proper tuning, outperforms the traditional approach with a fixed trade-off parameter. Thirdly, the MC-SPP for each frequency-band is used to obtain the MMSE estimate of the desired speech signal at the output, where we control the maximum amount of noise reduction based on our application. Experimental results on a large number of simulated scenarios show significant benefits of employing MC-SPP in terms of SNR improvements and speech distortion.