When the option is at the money slight changes in the volatility of the underlying asset will have greatest affect on the probability of the option being in the money at expiration. Can anyone explain? thanks

Do you remember the chart of volatility smile? if volatility=0, then the option always stays at the money. slight changes would cause the option value to be out of the money, or in the money. just think the change in slope from negative to positive is the greatest.