As you can see in the example I crafted below, the probability surface in the case of the squared exponential (Gaussian) Kernel as covariance function for Gaussian processes looks like a smooth density.
A good read about covariance functions in the context of Gaussian processes is Chapter 4 - Covariance Functions 
So, I'll be using R, specifically the
kernlab package for this example. There's a nice
gausspr function that accepts different kernel types as parameters. I'll be using the iris dataset as a binary classification problem with only two dimensions.
#let's use only two variables plus the target variable so we can accurately plot it
data = iris[, 3:5]
data$Species[data$Species == "virginica"] = "versicolor"
data$Species = factor(data$Species)
levels(data$Species) = c("setosa", "virginica OR versicolor")
#The fitting, you can change kernel and parameters, check the kernlab manual
fit = gausspr(Species~., data = data, kernel = "rbfdot")
pred = predict(fit, data)
N = 250L #integer that gives the number of unique values in each dimension of the grid
grid = expand.grid(
Petal.Length = seq(min(data$Petal.Length), max(data$Petal.Length), length.out = N),
Petal.Width = seq(min(data$Petal.Width), max(data$Petal.Width), length.out = N)
pred.grid = predict(fit, grid, type = "probabilities")[, 1, drop = FALSE]
#This maps the predictions a matrix representing the dimensions of data
pred.grid = matrix(pred.grid, ncol = N)
#The color part is thanks to http://www.r-bloggers.com/how-to-correctly-set-color-in-the-image-function/
tiff(filename = "Rplot_rbfdot.tiff")
image(unique(grid$Petal.Length), unique(grid$Petal.Width), pred.grid, useRaster = TRUE, col = ColorRamp,
ylab = "Petal.Width", xlab = "Petal.Length", main = "kernel = \"rbfdot\""
points(data[,1:2], pch = c(16,17)[as.numeric(pred)], col = adjustcolor("black", alpha = 0.5))
contour(unique(grid$Petal.Length), unique(grid$Petal.Width), pred.grid, add = TRUE,
levels = c(.4,.5,.6), labcex = 1, lwd = 1.75
legend("topleft", legend = levels(data$Species), pch = c(16,17), bg = "white")
These plots were produced with the above code.
 C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. © 2006 Massachusetts Institute of Technology. www.GaussianProcess.org/gpml