relation between acid and conjugate base and vice versa

[sanaz ahmadi- 2H]

I was hoping to get an explanation for why the stronger the acid, the weaker the conjugate base and also this same concept applying to strong bases. Does it have to do with Ka/Kb and pKa and pKb?

[Aarush_Maddela_3A]

Looking at it through the equilibrium concentrations might help. Stronger acids will dissociate more than weaker acids. This means there will be more product, and thus a higher ka for that acid. The reverse reaction with the conjugate base will not create as much product as the forwards reaction, since the forwards reaction involves a strong acid. This leads to the conjugate base having a lower kb, meaning a weaker conjugate base.