I was going through the introductory material by Horatiu in Ads-CFT. It says that $N+1$ D-branes are split into $N$ D-Branes and a probe D-Brane. The Wilson loop is located on the probe D-brane, which is at the Minkowski boundary of the AdS space.

The AdS space is given by $f^{-1/2}dx_{||}^2 + f^{1/2}(du^2 + d\Omega^2)$, where $f$ is the harmonic function = $\frac{R^4}{u^4}$.

My question is, what is causing this AdS metric (what is the source of the AdS space)? Is it the N D3 branes? or something else? If there is no source, then the space time would be flat.

Is there an assumption that the probe D3-brane is not modifying the metric of the AdS space at all?

Appreciate any clarification on this.