You could use the ggeffects package. Predicted probabilities for different subjects should work in the same way as for linear models, and is described in detail here.
However, currently you can't get confidence intervals for random effects when calculating predicted values for group levels / subjects... (any hints how to implement this are welcome!)
Example:
library(lme4)
#> Loading required package: Matrix
library(ggeffects)
data("cbpp")
set.seed(123)
cbpp$cont <- rnorm(nrow(cbpp))
# categorical predictor
m1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
me <- ggpredict(m1, terms = c("period", "herd [1,5,10,15]"), type = "re")
plot(me)
#> Loading required namespace: ggplot2

# continuous predictor
m2 <- glmer(cbind(incidence, size - incidence) ~ I(cont^2) + (1 | herd),
data = cbpp, family = binomial)
me <- ggpredict(m2, terms = c("cont", "herd [1,5,15]"), type = "re")
#> Model contains polynomial or cubic / quadratic terms. Consider using `terms="cont [all]"` to get smooth plots. See also package-vignette 'Marginal Effects at Specific Values'.
plot(me)

Created on 2020-06-17 by the reprex package (v0.3.0)