In a constant hazard rate model, the probability of default follows an exponential distribution, which has the "memoryless" property. This means that the probability of defaulting in the next year, given that the entity has survived up to the present, is exactly the same as the probability of defaulting in the first year from inception.

Given a constant hazard rate $\lambda = 0.09$, the cumulative probability of default within a $t = 1$ year period is given by: $PD = 1 - e^{-\lambda t}$

$PD = 1 - e^{-0.09 \times 1}$ $PD = 1 - 0.913931$ $PD = 0.086069$

Therefore, the conditional probability of defaulting before the end of the second year, given survival through the first year, is approximately 8.61%.