To find the conditional default probability, we plug the given values into the conditional cumulative default probability function:

1. $k_i = -1.6450`$2. $\beta_i = 0.60$3`.$m = -1.41$

$$p(-1.41) = \Phi\left( \frac{-1.6450 - 0.60 \times (-1.41)}{\sqrt{1 - 0.60^2}} \right)$$

Calculate the numerator: $-1.6450 - (-0.846) = -1.6450 + 0.846 = -0.799$

Calculate the denominator: $\sqrt{1 - 0.36} = \sqrt{0.64} = 0.80$

Divide numerator by denominator: $\frac{-0.799}{0.80} = -0.99875$

Find the standard normal CDF value for $Z = -0.99875$: $\Phi(-0.99875) \approx 0.15896$ or $15.90%$

Therefore, the conditional probability of default in this economic downturn is $15.90%$.