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To run three TVs, I'd suggest using an HDMI splitter to feed the two upstairs TVs, and a SCART-connected video sender to feed the one downstairs. Alternatively, 3- or 4-way HDMI splitters are available, but I have no experience of these.
When shopping, beware that an HDMI switch is not the same thing as an HDMI splitter. A switch is to connect two or more devices to one TV.