I am studying some event for a set of objects that can be plotted on a square $[0, 100] ^ 2$. I have used logistic regression to calculate probabilities that event occur for different objects and the output can be plotted as below:

We can observe a high density around point $(100, 50)$ and that basically the farther the less probable the event is. A distance to this point is one of the predictors, but there are also few others. What I am interested in is to capture a potential movement, i.e. how valuable is to move from point $A$ to point $B$. But I would like to reward also those movements which are made far from the point $(100, 50)$, not only those near to the point. And for the former the absolute increase in probability will be small even if a movement is pretty significant (long distance), while for the latter we can observe a large increase in probabilities even with a tiny move. So I think what I would need is to somehow nullify/smooth effect of distance from $(100, 50)$, i.e. make it less significant for calculating our movement gain. And I do not really know how to accomplish that. I cannot calculate the percentage gain, because this results in a really large gains. I think I need some monotonic transformation that would make a large probabilities lower and low probabilities higher. Any ideas what I could apply here?

Edit

@AlexFrancisco, I decided to edit a post to include an image that should help me in explanations. My question is: is there a way to restrict the parameters $a, b, c, M$ to such intervals that changing values within those intervals would make $1 - mathcalF(f(x))$ different concave functions ranging from identity (blue curve), by slightly concave function (purple curve) to maximally concave function (red curve)?

In other words, I would like to exclude those values of $a, b, c, M$ that makes $1 - mathcalF(f(x))$ not concave.

Assume that the density $f$ is positive on $[0, 100]^2$ and there exists a constant $M > 0$ such that $f(x) leqslant M$ for any $x in [0, 100]^2$. Two families of prototypical transformations are given first:$$
mathscrF_1(f)(x) = left( lnfracMf(x) right)^a, quad mathscrF_2(f)(x) = left( left( fracMf(x) right)^b - 1 right)^a,
$$
where $a, b > 0$ are parameters. To see the rationale, consider two families of density functions:$$
f_1(x) = M exp(-(d(x, x_0))^tfrac1a), quad f_2(x) = fracM((d(x, x_0))^tfrac1a + 1)^tfrac1b,
$$
where $x_0 = (100, 50)$ and $d$ is some distance function. Note that for $d(x, y) = sqrtsmash[b](x_1 - y_1)^2 + (x_2 - y_2)^2$, $a = dfrac12$, $b = dfrac23$, $f_1$ and $f_2$ are the density functions of bivariate normal distribution and that of bivariate Cauchy distribution, respectively. Solving $d(x, x_0)$ from $f_1$ and $f_2$ yields $d(x, x_0) = mathscrF_1(f_1)(x)$ and $d(x, x_0) = mathscrF_2(f_2)(x)$, respectively.

Now, since it may be unpractical to assume that $f$ is positive, or $f$ may be almost $0$ at points far from $x_0$, then it is useful to introduce another parameter $c > 0$, i.e.$$
mathscrF_1(f)(x) = left( lnfracM + cf(x) + c right)^a, quad mathscrF_2(f)(x) = left( left( fracM + cf(x) + c right)^b - 1 right)^a.
$$
After normalization,$$
mathscrF_1(f)(x) = left( fraclndfracM + cf(x) + clndfracM + cc right)^a, quad mathscrF_2(f)(x) = left( fracleft( dfracM + cf(x) + c right)^b - 1left( dfracM + cc right)^b - 1 right)^a.
$$