The odds we expect depend on our detection ability. Maybe there are thousands of these objects but we saw this one only because it passed so close to Earth.
There is fairly strong consensus in the astronomy community that possibly hundreds of Sednoid class objects exist, and those are in relatively normal orbits compared to things which are beyond solar escape velocity. But so far we've only found 3 or 4 Sednoids.
Sednoids orbiting in the kuiper belt are totally different from extrasolar objects on hyperbolic trajectories. Oamuamua passed inside Mercury's orbit.
Yes, but both classes of objects are very dificult to detect, due to distance, size and lack of brightness. We only detected the extrasolar object once it had already passed perihelion and was on its way out.
"Such an intrinsically faint body could be discovered only thanks to the close Earth flyby in October 2017, which created a tremendous opportunity for the first detailed characterization of a minor object of exosolar origin."