conditional expected number of success interpretation

Question

Suppose $f(k,n,\rho)$ is the pmf for the binomial distribution, then $$\sum_{r=0}^nf(r,n,\rho)r$$ is the expected number of successes. My question is, how can I interpret $$\sum_{r=M}^nf(r,n,\rho)r?$$ It's not the expected number of successes given there are at least $M$ successes... at least I don't think so. Follow up Question: Is there any interpretation to $$\frac{\sum_{r=M}^nf(r,n,\rho)r}{f(M-1,n,\rho)}?$$ Many thanks for all your help!