I think the above posters have all gotten it right. Both Ryanair and EasyJet make it very clear that they don't guarantee any connection of any kind, nor do they owe you anything if you don't make even a POSSIBLE connection -- even if it is entirely their fault that you don't.

They also won't check bags through a connection even if it is entirely on their own airline, as they want to charge you twice for the checked bag and also save costs by not putting any bag transfer procedure in place.