This study investigates the dependence of the coefficients of friction on the normal force produced by sliding a bare finger over different artificial skins with seven levels of hardness. The coefficient of friction was modeled as a power function of the normal force. An experimental study that involved sliding a finger over artificial skin surfaces was carried out under two conditions: the fingertip being wiped by a dry cloth or a cloth soaked in ethanol. Although the exponential term was assumed to be nearly constant for identical tribological conditions, we observed that the exponent varied randomly and could be negative, zero, or positive. This probabilistic behavior has not been explicitly analyzed in previous studies on human fingertips. The probability density function of the exponent depended on the moisture content of the finger. The exponent was either nearly zero or positive when the finger sliding on the skin surface was wiped with an alcohol-soaked cloth and dried. These findings play an important role in analyzing the frictional forces produced during skin–skin contact in terms of determining the root cause behind the random variations in the dependence of the coefficient of friction on the normal force.