To underline this point: we shot a red tesla into space about 2 years ago [1]. We cannot detect it any more. We'd need a telescope with a mirror of 15km to see it. Due to uncertainties accumulating, even if we'd had a scope like that, we'd probably not be able to point it exactly enough.
Oh, and that thing is mostly between the orbits of Mars and earth - much smaller search space than "the entire solar system"
So, some alien unmanned probe the likes of Voyager in large orbit around the Sun? Yeah, no chance in hell we'd detect that by random chance, we'd have to seriously upgrade our space infrastructure to even pretend 'monitoring' our close vicinity, let alone post-Jovian space. And we have virtually no knowledge of about half the distance between interstellar medium and the Sun, that's how limited we are to even modeling the closest star systems.
Edit: apparently double-post with aruggirello; I agree with him.