Assume that if $M$ launches a new e$-$trading platform, its price will go up to $$261.$ Else, $M$ price will go down to $$62.$ You are aware that $M$ shares are being traded at $$162.$ You also know that the risk$-$free rate is $5\%.$

What is the probability that M price will go down?

$***$ Please round your answer to the nearest three decimals $($i$.$e$.0\mathrm{.}512)$