It's a combination of intuition and experience in dealing with public servants (such as Errinwright and herself), and Errinwright's lack of convincing defense against her suspicions.
Errinwright and Mao were close personal friends. Errinwright never revealed this until Chrisjen confronted him about it in this scene.
While there is no ironclad proof from this conversation, Errinwright is really struggling to convince Avasarala that he doesn't know anything more than he's pretending to.
Avasarala also subtly mentions why she suspected Errinwright of colluding in that scene:
Tell [Mao's] children that the government is more powerful than any corporation, and the only reason they think it tilts the other way is because we, poor, public servants, are always looking for some fat, private-sectors payoff down the road. But I'm not looking. And by the time they can pull the strings to force me out, it'll be too late.
Avasarala has been in public office for most of her adult life, and is well aware of the private sector attracting public persons with a high profile (and well-connected network). This mirrors present day Earth, high profile political figures whose terms end often end up consulting/lobbying for a private firm.
Avasarala judged Errinwright to be the kind of person open to such an agreement, and she wasn't wrong about that. She has no conclusive proof yet, but she knows she's right.
Future hint: in season 5, there are a few scenes where Avasarala specifically argues that she should act on what she knows to be true, even if she can't convince others. It's something we see her do in most seasons, but in season 5 she explicitly describes her thought process.
Also note this review, commenting on how Avasarala cleverly threatens both Mao and Errinwright without doing so directly. It's the mark of a great politician and influencer.
Avasarala has one of her best scenes yet, confronting Errinwright in his office and demanding that he convince Jules-Pierre Mao to turn himself in. We haven’t seen her quite this forceful in a while, and what makes the confrontation especially effective is that she’s threatening both men without acknowledging that she knows any conspiracy has taken place.