In relativistic quantum theory, one sometimes considers integral equations
for a wave function $\psi(x_1,x_2)$ depending on two space-time points for two
particles. A serious issue with such equations is that, typically, the spatial
integral over $|\psi|^2$ is not conserved in time — which conflicts with the
basic probabilistic interpretation of quantum theory. However, here it is shown
that for a special class of integral equations with retarded interactions along
light cones, the global probability integral is, indeed, conserved on all
Cauchy surfaces. For another class of integral equations with more general
interaction kernels, asymptotic probability conservation from $t=-\infty$ to
$t=+\infty$ is shown to hold true. Moreover, a certain local conservation law
is deduced from the first result.
