  Probing deeper into the existing issues regarding the exit probability (EP)
in one dimensional dynamical models, we consider several models where the
states are represented by Ising spins and the information flows inwards. At
zero temperature, these systems evolve to either of two absorbing states. The
exit probability $E(x)$, which is the probability that the system ends up with
all spins up starting with $x$ fraction of up spins is found to have the
general form $E(x) = x^\alpha/\left[x^\alpha + (1-x)^\alpha\right]$. The exit
probability exponent $\alpha$ strongly depends on $r$, the range of
interaction, the symmetry of the model and the induced fluctuation. Even in a
nearest neighbour model, nonlinear form of EP can be obtained by controlling
the fluctuations and for the same range, different models give different
results for $\alpha$. Non-universal behaviour of the exit probability is thus
clearly established and the results are compared to existing studies in models
with outflow dynamics to distinguish the two dynamical scenarios.
