generally speaking: no measurement you make at point A is going to affect probabilities measured at point B outside its light-cone, because observable operators commute at spacelike separation (one of the basic properties of all relativistic quantum field theories).
But those measurements *can* affect things observed later on, at events late enough that classical information can propagate... and things like Bell's inequality prove that more is going on than just a slowly propagating hidden variable.
So this is all admittedly weird. Sometimes I phrase it as something like "quantum correlations can create nonlocally correlated *noise*... but you can't control it". Because if you could, either you could send messages backward in time, or relativity would break.