Assume a 1-year, zero coupon bond trading at $95. One year benchmark rate is 3%.

Recovery rate = 60%

So,

(60p+100(1-p))/1.03 = 95

(100-40p)/1.03 = 95

p = 5.38%, this is the risk neutral probability of default

Can someone please explain why they use the risk-free rate here? I understand to calculate the risk neutral probability, you would use a rate without any risk premiums which is the risk free rate, but why do we even calculate a “risk-neutral” probability? What is the point of it here? Thanks!