Let us consider a homotopy fibre sequence of connected spaces $A\rightarrow B\rightarrow C$ and let $K$ be a fixed field. Assume that the homology $H_{\ast}(A, K)$ is trivial and that $C$ is a nilpotent space (but not simply connected).

Does $H_{\ast}(B, K)\rightarrow H_{\ast}(C, K)$ have to be an isomorphism ?