The scenario describes a typical "volatility smile" or U-shaped implied volatility curve, where the implied volatility is lowest for at-the-money (ATM) options and progressively increases for both deep out-of-the-money (OTM) and deep in-the-money (ITM) options.

In the Black-Scholes-Merton model framework, a constant volatility implies a lognormal distribution of the underlying asset's returns. When the market prices ITM and OTM options with higher implied volatilities than ATM options, it means the market is pricing in a higher probability of extreme price movements in both directions compared to a lognormal distribution. Therefore, the market's implied probability distribution exhibits excess kurtosis (fat tails), meaning it has a heavier left tail and a heavier right tail than the lognormal distribution.