Orthogonal frequency division multiplexing (OFDM) has been widely adopted in dual-function radar-communication (DFRC) systems, where radar and communications are performed simultaneously with a common signal. However, with random communication symbols (CS) in DFRC, the transmit signal has a random ambiguity function that affects the radar's range-velocity estimation performance, whose influence is remained uncovered. Hence, this paper focuses on minimizing the outlier probability (OP) -- the probability of incorrectly estimating a target's range-velocity bin -- in OFDM DFRC w.r.t the CS probability distribution (i.e., the \emph{input distribution}). Conditioned on the CSs, the OP only depends on the CS magnitudes. Hence, we consider the following two schemes for the above optimization: CSs with (1) constant magnitude (phase shift keying input), and (2) random magnitude (Gaussian input). For (1), the problem reduces to the familiar power allocation design across OFDM's subcarriers and symbols, with uniform power allocation across subcarriers and a \emph{windowed} power allocation across symbols being near-optimal. For (2), the mean and variance of the Gaussian distribution at each subcarrier is optimized, with an additional communication constraint to avoid the zero-variance solution where no CSs are carried. We observe that subcarriers with strong communication channels feature strong variance (i.e., favour communications) while the others are characterized by a strong mean (favouring radar). However, the overall power allocation (i.e., the sum of mean and variance) across the OFDM subcarriers and symbols is similar to (1). Simulations show that CSs with random magnitudes degrade the sensing performance, but can be compensated significantly with the proposed input distribution optimization.