How can I reclassify a raster by zone?

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I have a raster layer of a river network containing weighted flow accumulation values and a raster layer of lakes (see image bellow). I want to replace the values of all the river pixel that fall into the lake by 0. How can I reclassify a raster by zone?

I tried to achieve the same result by doing this :

1. Use the Extract by Mask to have a layer of the river network that fall into the lakes.
2. Use the Raster Calculator to subtract the raster layer of the river network by the raster layer of the river network that fall into the lakes.

I though this would give the pixels that fall into the lakes the value of 0, but ALL the pixels get the value of 0 whether the pixel falls into a lake or not.

I have tried with ArcGIS 10.1 and QGIS 2.8.2 with the same result, so I'm probably doing something wrong.



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