Confidence interval for spline

Question

I am learning about spline variables for logit/Cox model and I generally notice that the confidence bands are narrow when odds/hazard ratio nears 1. What is the possible reason for this?

Attaching a sample chart for reference.

Edit: The code used to generate the above graph is based on a conditional logit model.

proc phreg data=have;
effect v1Spline=spline(v1/naturalcubic basis=tpf(noint) knotmethod=percentilelist(5 25 50 75 95);
model time*outcome(0)=v1Spline;
strata id;
run;