The first part of this paper presents exact probability distribution functions (PDF) of upcrossings in stationary first-order Markov processes for finite sample lengths. In the derivation of these PDF, the enumeration technique is used and the correctness of the results obtained is checked with the total probability of all the possible upcrossings, which has to equal unity for any sample length. Numerical calculations of these PDF on digital computers led to the condition that the expected number of crossings is linearly proportional to the truncation level probability. Hence, the proportionality factor is a function of the first-order autorun coefficient, which is intimately related to the first-order autocorrelation coefficient. The PDF are valid for stationary and dependent processes irrespective of their underlying probability distribution functions.