The signal detection thing is just dumb. Signals quickly fall in strength to background noise levels, so you need to broadcast a huge amount of power in a tight beam to overcome that over any significant distance. So basically, you're arguing that just because no ETs have bothered to pour a lot of resources into 1) finding us and learning of our existence, and 2) building a gigantic, power-consuming radio transmitter and directing it at us, that they must not exist.

The probes thing assumes that the ETs actually want to talk to us. That's a pretty huge assumption. We've had civilizations here on Earth which had no desire for outside contact (namely the Chinese during some of their dynasties). What makes you think the ETs are so intent on pouring resources into making artificially-intelligent probes to establish communications?

By that logic, WE don't exist, because we haven't bothered to do these things either.