This is Chapter 20, Q20.9 in the current (2021) version of the notes.
In your expression P(L <= V) >= 0.99, L represents the liability for the policy (ie benefits less premiums net of expenses) and V is the reserve. We want it to be highly likely that the reserve exceeds the liability.
The liability for the policy reduces over time. The liability is high at short durations as early death will mean that the sum assured will need to be paid even though only a few premiums will have been received. The liability is lower at longer durations as more premiums will have been received, and the death payment is further in the future.
So, as the liability reduces over time, the reserve is more likely to cover the liability at later durations, and the concern for the insurance company is the early death of the policyholder. This means that, for it to be highly likely that the reserve exceeds the liability, we need there to be a small probability of early death, ie P(K < r) < 0.01.
The condition P(K > r+1) >= 0.01 ensures that we find the first year where the probability switches from below 0.01 to above it.
